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I would like to know the name of the following conjecture: If $2^n$ and $3^n$ are both integers, must $n$ be an integer?

A friend mentioned that this was an unsolved problem. However, I am unable to find anything about this online.

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    try $n=\log_2 3=1.584962501$ Or are you saying that $2^n,3^n$ have to both be integers? – 2017-02-11
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    @lulu Yes, this seems to be the intent of the question – 2017-02-11
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    @Peter That makes sense. Looks hard...at least I have no immediate ideas. – 2017-02-11
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    This is an unsovled problem. https://www.quora.com/What-are-some-examples-of-deceptively-simple-looking-math-problems. – 2017-02-11

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