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 $P(x)−P(y)$ (Error compiling LaTeX. Unknown error_msg), then 107 divides $x-y$ . Show that 107 divides $m$ .

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

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2008 OIM Problems/Problem 3

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