Prove that if $n^x$ is an integer for every natural number $n$, then $x$ is also an integer.

Asked Dec 31 '14 at 01:30

Active Dec 31 '14 at 01:56

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Question above is self-explanatory.

Update $n$ is every natural number!

edited Dec 31 '14 at 01:56

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asked Dec 31 '14 at 01:30

user272651

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The statement is not true. Take $n=2$ and $x=\log_23$. – Edward Jiang Dec 31 '14 at 01:32
You're right! Sorry, I updated the question. Sorry for my english – user272651 Dec 31 '14 at 01:34
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If I recall correctly, this is an old Putnam problem... – Aryabhata Dec 31 '14 at 01:54

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