Python/project_euler/problem_63/sol1.py

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"""
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) = }")