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Let $P$ be a polynomial with integer coefficients such that for every positive integer $n$, $P(n)$ divides $2^n - 1$.

Show that $P(x) =1$ or $P(x) = -1$ for all $x$.

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    To be precise, it was Problem A5 on the 1972 exam. The exam is at http://mks.mff.cuni.cz/kalva/putnam/putn72.html, with a link to the solution.2012-09-23

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