2008 OIM Problems/Problem 3

Problem

Let $m$ and $n$ be integers such that the polynomial $P(x) = x^3 + mx + n$ has the following property: if $x$ and $y$ are integers and 107 divides $P(x)-P(y)$, then 107 divides $x-y$. Show that 107 divides $m$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions