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A long time ago I found a question on the internet that went a little like this:

Suppose that we have $n=2^k$ where $k\gt 3$. If $m$ is another number that is a combination of the digits of $2^k$, prove that $m$ cannot be a power of $2$.

I gave up on it a long time ago, but have now become interested in number theory and hope that someone could shed some light on this problem.

Edit: This is only for base 10.

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    When you say "a combination of the digits", you mean it is obtained by "shuffling them around", but using all of them? The usual mathematical term of that is "permutation" rather than "combination".2011-05-02
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    @Arturo Yes, you are correct. I meant to say that m is a permutation of the digits of n.2011-05-03

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