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Find all polynomials $P(x)\in\Bbb Z[x]$ such that for all $m,n\in\Bbb Z$, if $P(m)\mid P(n)$, then $m\mid n$.

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What have you tried? –  Mark Bennet Jun 1 '12 at 15:32
If this is homework, tag it as such. –  lhf Jun 1 '12 at 15:34
Welcome to math.SE. Since you are new, I want to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. If this is homework, please add the [homework] tag; people will still help, so don't worry. Also, many users find the use of the imperative ("Find", "Show", etc) to be rude when asking for help. Please consider rewriting your post. –  Arturo Magidin Jun 1 '12 at 16:33

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