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