Created problem_63 in project_euler

project_euler/problem_63/__init__.py

@@ -0,0 +1 @@
+#

project_euler/problem_63/sol1.py

@@ -0,0 +1,34 @@
+"""
+The 5-digit number, 16807=75, is also a fifth power. Similarly, the 9-digit number,
+134217728=89, is a ninth power.
+How many n-digit positive integers exist which are also an nth power?
+"""
+
+"""
+The maximum base can be 9 because all n-digit numbers < 10^n.
+Now 9**23 has 22 digits so the maximum power can be 22.
+Using these conclusions, we will calculate the result.
+"""
+
+
+def compute_nums(max_base: int = 10, max_power: int = 22) -> int:
+    """
+    Returns the count of all n-digit numbers which are nth power
+    >>> compute_nums(10, 22)
+    49
+    >>> compute_nums(0, 0)
+    0
+    >>> compute_nums(1, 1)
+    0
+    >>> compute_nums(-1, -1)
+    0
+    """
+    bases = range(1, max_base)
+    powers = range(1, max_power)
+    return sum(
+        1 for power in powers for base in bases if len(str((base ** power))) == power
+    )
+
+
+if __name__ == "__main__":
+    print(f"{compute_nums(10, 22) = }")