From c31911963df6ded34c57931477fb2ad8ac73dc6a Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Thu, 31 Aug 2023 12:06:16 +0100
Subject: [PATCH 01/20] Created harshad_numbers.py

---
 maths/harshad_numbers.py | 132 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 132 insertions(+)
 create mode 100644 maths/harshad_numbers.py

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
new file mode 100644
index 000000000000..45175fbb4eac
--- /dev/null
+++ b/maths/harshad_numbers.py
@@ -0,0 +1,132 @@
+"""
+A harshad number in a base n is an integer divisible by the sum of its digits in that base.
+Reference: https://en.wikipedia.org/wiki/Harshad_number
+"""
+
+
+def int_to_base(number, base_of_interest):
+    digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+    result = ""
+
+    while number > 0:
+        number, remainder = divmod(number, base_of_interest)
+        result = digits[remainder] + result
+    
+    if result == "":
+        result = "0"
+    
+    return result
+
+
+def sum_of_digits(num: int, base_of_interest: int):
+    """
+    Calculate the sum of digit values in a positive integer
+    converted to the given 'base_of_interest'.
+    Where 'base_of_interest' ranges from 2 to 36.
+
+    Examples:
+    >>> sum_of_digits(103, 12)
+    '13'
+    >>> sum_of_digits(1275, 4)
+    '30'
+    >>> sum_of_digits(6645, 2)
+    '1001'
+    >>> # bases beyond 36 and below 2 will error
+    >>> sum_of_digits(543, 1)
+    Traceback (most recent call last):
+        ...
+    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
+    >>> sum_of_digits(543, 37)
+    Traceback (most recent call last):
+        ...
+    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
+    """
+
+    if ((base_of_interest > 36) or (base_of_interest < 2)):
+        raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
+
+    num = int_to_base(num, base_of_interest)
+    sum = 0
+    for char in num:
+        sum += int(char, base_of_interest)
+    sum = int_to_base(sum, base_of_interest)
+    return sum
+
+
+def all_harshad_numbers(num: int, base_of_interest: int):
+    """
+    Finds all Harshad numbers smaller than num in base 'base_of_interest'.
+    Where 'base_of_interest' ranges from 2 to 36.
+
+    Examples:
+    >>> all_harshad_numbers(15, 2)
+    (7, ['1', '10', '100', '110', '1000', '1010', '1100'])
+    >>> all_harshad_numbers(25, 34)
+    (24, ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O'])
+    >>> all_harshad_numbers(12, 4)
+    (7, ['1', '2', '3', '10', '12', '20', '21'])
+    >>> # bases beyond 36 and below 2 will error
+    >>> all_harshad_numbers(234, 37)
+    Traceback (most recent call last):
+        ...
+    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
+    >>> all_harshad_numbers(234, 1)
+    Traceback (most recent call last):
+        ...
+    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
+    """
+
+    if ((base_of_interest > 36) or (base_of_interest < 2)):
+        raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
+
+    result = 0
+    numbers = []
+    if (num >= 0):
+        for i in range(1, num):
+            y = sum_of_digits(i, base_of_interest)
+            if (i % int(y, base_of_interest) == 0):
+                result += 1
+                numbers.append(int_to_base(i, base_of_interest))
+
+    return result, numbers
+
+
+def is_harshad_number(num: int, base_of_interest: int):
+    """
+    Determines whether n in base 'base_of_interest' is a harshad number.
+    Where 'base_of_interest' ranges from 2 to 36.
+
+    Examples:
+    >>> is_harshad_number(18, 10)
+    True
+    >>> is_harshad_number(21, 10)
+    True
+    >>> is_harshad_number(-21, 5)
+    False
+    >>> # bases beyond 36 and below 2 will error
+    >>> is_harshad_number(45, 37)
+    Traceback (most recent call last):
+        ...
+    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
+    >>> is_harshad_number(45, 1)
+    Traceback (most recent call last):
+        ...
+    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
+    """
+
+    if ((base_of_interest > 36) or (base_of_interest < 2)):
+        raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
+
+    if (num >= 0):
+        n = int_to_base(num, base_of_interest)
+        d = sum_of_digits(num, base_of_interest)
+        if (int(n, base_of_interest) % int(d, base_of_interest) == 0):
+            return True
+
+    return False
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
\ No newline at end of file

From e10bc546ff6ae1fd7cee681a27af3be5a31961a5 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Thu, 31 Aug 2023 11:07:56 +0000
Subject: [PATCH 02/20] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/harshad_numbers.py | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index 45175fbb4eac..4189aa48a80f 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -11,10 +11,10 @@ def int_to_base(number, base_of_interest):
     while number > 0:
         number, remainder = divmod(number, base_of_interest)
         result = digits[remainder] + result
-    
+
     if result == "":
         result = "0"
-    
+
     return result
 
 
@@ -42,7 +42,7 @@ def sum_of_digits(num: int, base_of_interest: int):
     ValueError: 'base_of_interest' must be between 36 and 2 inclusive
     """
 
-    if ((base_of_interest > 36) or (base_of_interest < 2)):
+    if (base_of_interest > 36) or (base_of_interest < 2):
         raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
 
     num = int_to_base(num, base_of_interest)
@@ -76,15 +76,15 @@ def all_harshad_numbers(num: int, base_of_interest: int):
     ValueError: 'base_of_interest' must be between 36 and 2 inclusive
     """
 
-    if ((base_of_interest > 36) or (base_of_interest < 2)):
+    if (base_of_interest > 36) or (base_of_interest < 2):
         raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
 
     result = 0
     numbers = []
-    if (num >= 0):
+    if num >= 0:
         for i in range(1, num):
             y = sum_of_digits(i, base_of_interest)
-            if (i % int(y, base_of_interest) == 0):
+            if i % int(y, base_of_interest) == 0:
                 result += 1
                 numbers.append(int_to_base(i, base_of_interest))
 
@@ -114,13 +114,13 @@ def is_harshad_number(num: int, base_of_interest: int):
     ValueError: 'base_of_interest' must be between 36 and 2 inclusive
     """
 
-    if ((base_of_interest > 36) or (base_of_interest < 2)):
+    if (base_of_interest > 36) or (base_of_interest < 2):
         raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
 
-    if (num >= 0):
+    if num >= 0:
         n = int_to_base(num, base_of_interest)
         d = sum_of_digits(num, base_of_interest)
-        if (int(n, base_of_interest) % int(d, base_of_interest) == 0):
+        if int(n, base_of_interest) % int(d, base_of_interest) == 0:
             return True
 
     return False
@@ -129,4 +129,4 @@ def is_harshad_number(num: int, base_of_interest: int):
 if __name__ == "__main__":
     import doctest
 
-    doctest.testmod()
\ No newline at end of file
+    doctest.testmod()

From deec6d43eb2b16d0332a6b89adad097f5b4fa376 Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Thu, 31 Aug 2023 12:19:57 +0100
Subject: [PATCH 03/20] Update harshad_numbers.py

Fixed a few errors
---
 maths/harshad_numbers.py | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index 4189aa48a80f..2f5b696c03a9 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -1,5 +1,5 @@
 """
-A harshad number in a base n is an integer divisible by the sum of its digits in that base.
+A Harshad number is divisible by the sum of its digits in any base n.
 Reference: https://en.wikipedia.org/wiki/Harshad_number
 """
 
@@ -46,11 +46,11 @@ def sum_of_digits(num: int, base_of_interest: int):
         raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
 
     num = int_to_base(num, base_of_interest)
-    sum = 0
+    res = 0
     for char in num:
-        sum += int(char, base_of_interest)
-    sum = int_to_base(sum, base_of_interest)
-    return sum
+        res += int(char, base_of_interest)
+    res = int_to_base(res, base_of_interest)
+    return res
 
 
 def all_harshad_numbers(num: int, base_of_interest: int):
@@ -61,8 +61,8 @@ def all_harshad_numbers(num: int, base_of_interest: int):
     Examples:
     >>> all_harshad_numbers(15, 2)
     (7, ['1', '10', '100', '110', '1000', '1010', '1100'])
-    >>> all_harshad_numbers(25, 34)
-    (24, ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O'])
+    >>> all_harshad_numbers(12, 34)
+    (11, ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B'])
     >>> all_harshad_numbers(12, 4)
     (7, ['1', '2', '3', '10', '12', '20', '21'])
     >>> # bases beyond 36 and below 2 will error

From fcb5639f11938c3af25a2abb9396004ff6329619 Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Thu, 31 Aug 2023 12:29:38 +0100
Subject: [PATCH 04/20] Update harshad_numbers.py

Added function type hints
---
 maths/harshad_numbers.py | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index 2f5b696c03a9..0c830ba5372b 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -3,8 +3,10 @@
 Reference: https://en.wikipedia.org/wiki/Harshad_number
 """
 
+from typing import Tuple, List
 
-def int_to_base(number, base_of_interest):
+
+def int_to_base(number: int, base_of_interest: int) -> str:
     digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
     result = ""
 
@@ -18,7 +20,7 @@ def int_to_base(number, base_of_interest):
     return result
 
 
-def sum_of_digits(num: int, base_of_interest: int):
+def sum_of_digits(num: int, base_of_interest: int) -> str:
     """
     Calculate the sum of digit values in a positive integer
     converted to the given 'base_of_interest'.
@@ -53,7 +55,7 @@ def sum_of_digits(num: int, base_of_interest: int):
     return res
 
 
-def all_harshad_numbers(num: int, base_of_interest: int):
+def all_harshad_numbers(num: int, base_of_interest: int) -> Tuple[int, List[str]]:
     """
     Finds all Harshad numbers smaller than num in base 'base_of_interest'.
     Where 'base_of_interest' ranges from 2 to 36.
@@ -91,7 +93,7 @@ def all_harshad_numbers(num: int, base_of_interest: int):
     return result, numbers
 
 
-def is_harshad_number(num: int, base_of_interest: int):
+def is_harshad_number(num: int, base_of_interest: int) -> bool:
     """
     Determines whether n in base 'base_of_interest' is a harshad number.
     Where 'base_of_interest' ranges from 2 to 36.

From 44eb28623bff4700d879f2fc623cf1bf58854acb Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Thu, 31 Aug 2023 12:33:15 +0100
Subject: [PATCH 05/20] Update harshad_numbers.py

Fixed depreciated Tuple and List usage
---
 maths/harshad_numbers.py | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index 0c830ba5372b..7edf639794b2 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -3,8 +3,6 @@
 Reference: https://en.wikipedia.org/wiki/Harshad_number
 """
 
-from typing import Tuple, List
-
 
 def int_to_base(number: int, base_of_interest: int) -> str:
     digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
@@ -55,7 +53,7 @@ def sum_of_digits(num: int, base_of_interest: int) -> str:
     return res
 
 
-def all_harshad_numbers(num: int, base_of_interest: int) -> Tuple[int, List[str]]:
+def all_harshad_numbers(num: int, base_of_interest: int) -> tuple[int, list[str]]:
     """
     Finds all Harshad numbers smaller than num in base 'base_of_interest'.
     Where 'base_of_interest' ranges from 2 to 36.

From ad09b82e537d8e8c1c23cdd0cbabc0506296607a Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Thu, 31 Aug 2023 12:41:47 +0100
Subject: [PATCH 06/20] Update harshad_numbers.py

Fixed incompatible types in assignments
---
 maths/harshad_numbers.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index 7edf639794b2..eac554a95bf0 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -45,9 +45,9 @@ def sum_of_digits(num: int, base_of_interest: int) -> str:
     if (base_of_interest > 36) or (base_of_interest < 2):
         raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
 
-    num = int_to_base(num, base_of_interest)
+    num_str = int_to_base(num, base_of_interest)
     res = 0
-    for char in num:
+    for char in num_str:
         res += int(char, base_of_interest)
     res = int_to_base(res, base_of_interest)
     return res

From 3d00dad53518e3570aa4771667a8a51e567106d4 Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Thu, 31 Aug 2023 12:44:53 +0100
Subject: [PATCH 07/20] Update harshad_numbers.py

Fixed incompatible type assignments
---
 maths/harshad_numbers.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index eac554a95bf0..489be3c29cfc 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -49,8 +49,8 @@ def sum_of_digits(num: int, base_of_interest: int) -> str:
     res = 0
     for char in num_str:
         res += int(char, base_of_interest)
-    res = int_to_base(res, base_of_interest)
-    return res
+    res_str = int_to_base(res, base_of_interest)
+    return res_str
 
 
 def all_harshad_numbers(num: int, base_of_interest: int) -> tuple[int, list[str]]:

From 4d1a89cd294783db1b01d253eee817a7f4774ffc Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Tue, 5 Sep 2023 11:06:53 +0100
Subject: [PATCH 08/20] Update maths/harshad_numbers.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
---
 maths/harshad_numbers.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index 489be3c29cfc..aba49674b508 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -4,7 +4,7 @@
 """
 
 
-def int_to_base(number: int, base_of_interest: int) -> str:
+def int_to_base(number: int, base: int) -> str:
     digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
     result = ""
 

From 21a703d4952e7093ab54a989f00119aba81816a7 Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Tue, 5 Sep 2023 11:07:07 +0100
Subject: [PATCH 09/20] Update maths/harshad_numbers.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
---
 maths/harshad_numbers.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index aba49674b508..8a5beb6f5ff2 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -18,7 +18,7 @@ def int_to_base(number: int, base: int) -> str:
     return result
 
 
-def sum_of_digits(num: int, base_of_interest: int) -> str:
+def sum_of_digits(num: int, base: int) -> str:
     """
     Calculate the sum of digit values in a positive integer
     converted to the given 'base_of_interest'.

From 1584436dfa7150c357973d45bac5e046c0e47bb6 Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Tue, 5 Sep 2023 19:24:02 +0100
Subject: [PATCH 10/20] Raised Value Error for negative inputs

---
 maths/harshad_numbers.py | 19 +++++++++++--------
 1 file changed, 11 insertions(+), 8 deletions(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index 8a5beb6f5ff2..b000bc0759ff 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -8,6 +8,9 @@ def int_to_base(number: int, base: int) -> str:
     digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
     result = ""
 
+    if number < 0:
+        raise ValueError("number must be a positive integer")
+
     while number > 0:
         number, remainder = divmod(number, base_of_interest)
         result = digits[remainder] + result
@@ -21,8 +24,8 @@ def int_to_base(number: int, base: int) -> str:
 def sum_of_digits(num: int, base: int) -> str:
     """
     Calculate the sum of digit values in a positive integer
-    converted to the given 'base_of_interest'.
-    Where 'base_of_interest' ranges from 2 to 36.
+    converted to the given 'base'.
+    Where 'base' ranges from 2 to 36.
 
     Examples:
     >>> sum_of_digits(103, 12)
@@ -39,17 +42,17 @@ def sum_of_digits(num: int, base: int) -> str:
     >>> sum_of_digits(543, 37)
     Traceback (most recent call last):
         ...
-    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
+    ValueError: 'base' must be between 36 and 2 inclusive
     """
 
-    if (base_of_interest > 36) or (base_of_interest < 2):
-        raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
+    if (base > 36) or (base < 2):
+        raise ValueError("'base' must be between 36 and 2 inclusive")
 
-    num_str = int_to_base(num, base_of_interest)
+    num_str = int_to_base(num, base)
     res = 0
     for char in num_str:
-        res += int(char, base_of_interest)
-    res_str = int_to_base(res, base_of_interest)
+        res += int(char, base)
+    res_str = int_to_base(res, base)
     return res_str
 
 

From 7b9809cb971c0406bad16abe60939a8bff3eecdc Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Tue, 5 Sep 2023 19:27:51 +0100
Subject: [PATCH 11/20] Update maths/harshad_numbers.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
---
 maths/harshad_numbers.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index b000bc0759ff..3c21d93ff27d 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -56,7 +56,7 @@ def sum_of_digits(num: int, base: int) -> str:
     return res_str
 
 
-def all_harshad_numbers(num: int, base_of_interest: int) -> tuple[int, list[str]]:
+def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
     """
     Finds all Harshad numbers smaller than num in base 'base_of_interest'.
     Where 'base_of_interest' ranges from 2 to 36.

From 03d0296aaf7a946f98a3ba3c11ade2b3d812b1b3 Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Tue, 5 Sep 2023 19:31:09 +0100
Subject: [PATCH 12/20] Update maths/harshad_numbers.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
---
 maths/harshad_numbers.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index 3c21d93ff27d..286d9f305384 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -94,7 +94,7 @@ def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
     return result, numbers
 
 
-def is_harshad_number(num: int, base_of_interest: int) -> bool:
+def is_harshad_number_in_base(num: int, base: int) -> bool:
     """
     Determines whether n in base 'base_of_interest' is a harshad number.
     Where 'base_of_interest' ranges from 2 to 36.

From 2974289dc52e2c34e2f4dc9c18111e6363038bef Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Tue, 5 Sep 2023 19:31:28 +0100
Subject: [PATCH 13/20] Update maths/harshad_numbers.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
---
 maths/harshad_numbers.py | 11 +++++------
 1 file changed, 5 insertions(+), 6 deletions(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index 286d9f305384..2d0340fa2f01 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -120,13 +120,12 @@ def is_harshad_number_in_base(num: int, base: int) -> bool:
     if (base_of_interest > 36) or (base_of_interest < 2):
         raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
 
-    if num >= 0:
-        n = int_to_base(num, base_of_interest)
-        d = sum_of_digits(num, base_of_interest)
-        if int(n, base_of_interest) % int(d, base_of_interest) == 0:
-            return True
+    if num < 0:
+        return False
 
-    return False
+    n = int_to_base(num, base_of_interest)
+    d = sum_of_digits(num, base_of_interest)
+    return int(n, base_of_interest) % int(d, base_of_interest) == 0
 
 
 if __name__ == "__main__":

From 6ebaf2589e42e6c9f7abb64139c5fba9a994d14d Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Tue, 5 Sep 2023 19:38:14 +0100
Subject: [PATCH 14/20] Update harshad_numbers.py

---
 maths/harshad_numbers.py | 61 ++++++++++++++++++++--------------------
 1 file changed, 31 insertions(+), 30 deletions(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index 2d0340fa2f01..91f302f69526 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -1,5 +1,6 @@
 """
-A Harshad number is divisible by the sum of its digits in any base n.
+A harshad number (or more specifically an n-harshad number) is a number that's 
+divisible by the sum of its digits in some given base n.
 Reference: https://en.wikipedia.org/wiki/Harshad_number
 """
 
@@ -12,7 +13,7 @@ def int_to_base(number: int, base: int) -> str:
         raise ValueError("number must be a positive integer")
 
     while number > 0:
-        number, remainder = divmod(number, base_of_interest)
+        number, remainder = divmod(number, base)
         result = digits[remainder] + result
 
     if result == "":
@@ -58,74 +59,74 @@ def sum_of_digits(num: int, base: int) -> str:
 
 def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
     """
-    Finds all Harshad numbers smaller than num in base 'base_of_interest'.
-    Where 'base_of_interest' ranges from 2 to 36.
+    Finds all Harshad numbers smaller than num in base 'base'.
+    Where 'base' ranges from 2 to 36.
 
     Examples:
-    >>> all_harshad_numbers(15, 2)
+    >>> harshad_numbers_in_base(15, 2)
     (7, ['1', '10', '100', '110', '1000', '1010', '1100'])
-    >>> all_harshad_numbers(12, 34)
+    >>> harshad_numbers_in_base(12, 34)
     (11, ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B'])
-    >>> all_harshad_numbers(12, 4)
+    >>> harshad_numbers_in_base(12, 4)
     (7, ['1', '2', '3', '10', '12', '20', '21'])
     >>> # bases beyond 36 and below 2 will error
-    >>> all_harshad_numbers(234, 37)
+    >>> harshad_numbers_in_base(234, 37)
     Traceback (most recent call last):
         ...
-    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
-    >>> all_harshad_numbers(234, 1)
+    ValueError: 'base' must be between 36 and 2 inclusive
+    >>> harshad_numbers_in_base(234, 1)
     Traceback (most recent call last):
         ...
-    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
+    ValueError: 'base' must be between 36 and 2 inclusive
     """
 
-    if (base_of_interest > 36) or (base_of_interest < 2):
-        raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
+    if (base > 36) or (base < 2):
+        raise ValueError("'base' must be between 36 and 2 inclusive")
 
     result = 0
     numbers = []
     if num >= 0:
         for i in range(1, num):
-            y = sum_of_digits(i, base_of_interest)
-            if i % int(y, base_of_interest) == 0:
+            y = sum_of_digits(i, base)
+            if i % int(y, base) == 0:
                 result += 1
-                numbers.append(int_to_base(i, base_of_interest))
+                numbers.append(int_to_base(i, base))
 
     return result, numbers
 
 
 def is_harshad_number_in_base(num: int, base: int) -> bool:
     """
-    Determines whether n in base 'base_of_interest' is a harshad number.
-    Where 'base_of_interest' ranges from 2 to 36.
+    Determines whether n in base 'base' is a harshad number.
+    Where 'base' ranges from 2 to 36.
 
     Examples:
-    >>> is_harshad_number(18, 10)
+    >>> is_harshad_number_in_base(18, 10)
     True
-    >>> is_harshad_number(21, 10)
+    >>> is_harshad_number_in_base(21, 10)
     True
-    >>> is_harshad_number(-21, 5)
+    >>> is_harshad_number_in_base(-21, 5)
     False
     >>> # bases beyond 36 and below 2 will error
-    >>> is_harshad_number(45, 37)
+    >>> is_harshad_number_in_base(45, 37)
     Traceback (most recent call last):
         ...
-    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
-    >>> is_harshad_number(45, 1)
+    ValueError: 'base' must be between 36 and 2 inclusive
+    >>> is_harshad_number_in_base(45, 1)
     Traceback (most recent call last):
         ...
-    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
+    ValueError: 'base' must be between 36 and 2 inclusive
     """
 
-    if (base_of_interest > 36) or (base_of_interest < 2):
-        raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
+    if (base > 36) or (base < 2):
+        raise ValueError("'base' must be between 36 and 2 inclusive")
 
     if num < 0:
         return False
 
-    n = int_to_base(num, base_of_interest)
-    d = sum_of_digits(num, base_of_interest)
-    return int(n, base_of_interest) % int(d, base_of_interest) == 0
+    n = int_to_base(num, base)
+    d = sum_of_digits(num, base)
+    return int(n, base) % int(d, base) == 0
 
 
 if __name__ == "__main__":

From 04f1e2b19e29b17e8f8c89ccc14d41582665e84e Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 5 Sep 2023 18:39:33 +0000
Subject: [PATCH 15/20] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/harshad_numbers.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index 91f302f69526..eabd31f165d4 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -1,5 +1,5 @@
 """
-A harshad number (or more specifically an n-harshad number) is a number that's 
+A harshad number (or more specifically an n-harshad number) is a number that's
 divisible by the sum of its digits in some given base n.
 Reference: https://en.wikipedia.org/wiki/Harshad_number
 """

From 6b0243c5f2f01b6eda450e884ef0bc5bfa8b4296 Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Tue, 5 Sep 2023 19:52:20 +0100
Subject: [PATCH 16/20] Update harshad_numbers.py

---
 maths/harshad_numbers.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index eabd31f165d4..f23fea57ff0a 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -85,8 +85,8 @@ def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
 
     result = 0
     numbers = []
-    if num >= 0:
-        for i in range(1, num):
+    if limit >= 0:
+        for i in range(1, limit):
             y = sum_of_digits(i, base)
             if i % int(y, base) == 0:
                 result += 1

From 385c29495423ffbf87f49d953928613d372a7cb4 Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Wed, 6 Sep 2023 01:29:01 +0100
Subject: [PATCH 17/20] Update harshad_numbers.py

---
 maths/harshad_numbers.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index f23fea57ff0a..7ee058875e24 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -39,7 +39,7 @@ def sum_of_digits(num: int, base: int) -> str:
     >>> sum_of_digits(543, 1)
     Traceback (most recent call last):
         ...
-    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
+    ValueError: 'base' must be between 36 and 2 inclusive
     >>> sum_of_digits(543, 37)
     Traceback (most recent call last):
         ...

From edf0036cda4ec9abc750cabcccd517a684e33f0b Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Wed, 6 Sep 2023 01:34:45 +0100
Subject: [PATCH 18/20] Update harshad_numbers.py

---
 maths/harshad_numbers.py | 10 ++++------
 1 file changed, 4 insertions(+), 6 deletions(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index 7ee058875e24..6f084289af4b 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -64,11 +64,11 @@ def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
 
     Examples:
     >>> harshad_numbers_in_base(15, 2)
-    (7, ['1', '10', '100', '110', '1000', '1010', '1100'])
+    ['1', '10', '100', '110', '1000', '1010', '1100']
     >>> harshad_numbers_in_base(12, 34)
-    (11, ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B'])
+    ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B']
     >>> harshad_numbers_in_base(12, 4)
-    (7, ['1', '2', '3', '10', '12', '20', '21'])
+    ['1', '2', '3', '10', '12', '20', '21']
     >>> # bases beyond 36 and below 2 will error
     >>> harshad_numbers_in_base(234, 37)
     Traceback (most recent call last):
@@ -83,16 +83,14 @@ def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
     if (base > 36) or (base < 2):
         raise ValueError("'base' must be between 36 and 2 inclusive")
 
-    result = 0
     numbers = []
     if limit >= 0:
         for i in range(1, limit):
             y = sum_of_digits(i, base)
             if i % int(y, base) == 0:
-                result += 1
                 numbers.append(int_to_base(i, base))
 
-    return result, numbers
+    return numbers
 
 
 def is_harshad_number_in_base(num: int, base: int) -> bool:

From 8dbfa37288ac8c8217f6762e0121ffd11a9af8ab Mon Sep 17 00:00:00 2001
From: David Ekong <66387173+davidekong@users.noreply.github.com>
Date: Wed, 6 Sep 2023 13:03:28 +0100
Subject: [PATCH 19/20] Update harshad_numbers.py

Added doc test to int_to_base, fixed nested loop, other minor changes
---
 maths/harshad_numbers.py | 73 +++++++++++++++++++++++++++-------------
 1 file changed, 49 insertions(+), 24 deletions(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index 6f084289af4b..7e1347d50661 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -6,6 +6,31 @@
 
 
 def int_to_base(number: int, base: int) -> str:
+    """
+    Convert a given positive decimal integer to base 'base'.
+    Where 'base' ranges from 2 to 36.
+
+    Examples:
+    >>> int_to_base(23, 2)
+    '10111'
+    >>> int_to_base(58, 5)
+    '213'
+    >>> int_to_base(167, 16)
+    'A7'
+    >>> # bases below 2 and beyond 36 will error
+    >>> int_to_base(98, 1)
+    Traceback (most recent call last):
+        ...
+    ValueError: 'base' must be between 2 and 36 inclusive
+    >>> int_to_base(98, 37)
+    Traceback (most recent call last):
+        ...
+    ValueError: 'base' must be between 2 and 36 inclusive
+    """
+
+    if base < 2 or base > 36:
+        raise ValueError("'base' must be between 2 and 36 inclusive")
+
     digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
     result = ""
 
@@ -35,24 +60,22 @@ def sum_of_digits(num: int, base: int) -> str:
     '30'
     >>> sum_of_digits(6645, 2)
     '1001'
-    >>> # bases beyond 36 and below 2 will error
+    >>> # bases below 2 and beyond 36 will error
     >>> sum_of_digits(543, 1)
     Traceback (most recent call last):
         ...
-    ValueError: 'base' must be between 36 and 2 inclusive
+    ValueError: 'base' must be between 2 and 36 inclusive
     >>> sum_of_digits(543, 37)
     Traceback (most recent call last):
         ...
-    ValueError: 'base' must be between 36 and 2 inclusive
+    ValueError: 'base' must be between 2 and 36 inclusive
     """
 
-    if (base > 36) or (base < 2):
-        raise ValueError("'base' must be between 36 and 2 inclusive")
+    if base < 2 or base > 36:
+        raise ValueError("'base' must be between 2 and 36 inclusive")
 
     num_str = int_to_base(num, base)
-    res = 0
-    for char in num_str:
-        res += int(char, base)
+    res = sum(int(char, base) for char in num_str)
     res_str = int_to_base(res, base)
     return res_str
 
@@ -69,26 +92,28 @@ def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
     ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B']
     >>> harshad_numbers_in_base(12, 4)
     ['1', '2', '3', '10', '12', '20', '21']
-    >>> # bases beyond 36 and below 2 will error
+    >>> # bases below 2 and beyond 36 will error
     >>> harshad_numbers_in_base(234, 37)
     Traceback (most recent call last):
         ...
-    ValueError: 'base' must be between 36 and 2 inclusive
+    ValueError: 'base' must be between 2 and 36 inclusive
     >>> harshad_numbers_in_base(234, 1)
     Traceback (most recent call last):
         ...
-    ValueError: 'base' must be between 36 and 2 inclusive
+    ValueError: 'base' must be between 2 and 36 inclusive
     """
 
-    if (base > 36) or (base < 2):
-        raise ValueError("'base' must be between 36 and 2 inclusive")
+    if base < 2 or base > 36:
+        raise ValueError("'base' must be between 2 and 36 inclusive")
 
-    numbers = []
-    if limit >= 0:
-        for i in range(1, limit):
-            y = sum_of_digits(i, base)
-            if i % int(y, base) == 0:
-                numbers.append(int_to_base(i, base))
+    if limit < 0:
+        return []
+    
+    numbers = [
+        int_to_base(i, base)
+        for i in range(1, limit)
+        if i % int(sum_of_digits(i, base), base) == 0
+    ]
 
     return numbers
 
@@ -105,19 +130,19 @@ def is_harshad_number_in_base(num: int, base: int) -> bool:
     True
     >>> is_harshad_number_in_base(-21, 5)
     False
-    >>> # bases beyond 36 and below 2 will error
+    >>> # bases below 2 and beyond 36 will error
     >>> is_harshad_number_in_base(45, 37)
     Traceback (most recent call last):
         ...
-    ValueError: 'base' must be between 36 and 2 inclusive
+    ValueError: 'base' must be between 2 and 36 inclusive
     >>> is_harshad_number_in_base(45, 1)
     Traceback (most recent call last):
         ...
-    ValueError: 'base' must be between 36 and 2 inclusive
+    ValueError: 'base' must be between 2 and 36 inclusive
     """
 
-    if (base > 36) or (base < 2):
-        raise ValueError("'base' must be between 36 and 2 inclusive")
+    if base < 2 or base > 36:
+        raise ValueError("'base' must be between 2 and 36 inclusive")
 
     if num < 0:
         return False

From d4d9c7c2fd465e139ed37ed80ae9961a7df6c97e Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 6 Sep 2023 12:04:03 +0000
Subject: [PATCH 20/20] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/harshad_numbers.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/maths/harshad_numbers.py b/maths/harshad_numbers.py
index 7e1347d50661..050c69e0bd15 100644
--- a/maths/harshad_numbers.py
+++ b/maths/harshad_numbers.py
@@ -108,7 +108,7 @@ def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
 
     if limit < 0:
         return []
-    
+
     numbers = [
         int_to_base(i, base)
         for i in range(1, limit)