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prime number dividing $a^N+b^n+c^N$ !CMO 2015 P5

Source: canadian mathematical olympiad

April 24, 2015
number theoryprime numbers

Problem Statement

Let pp be a prime number for which p−12\frac{p-1}{2} is also prime, and let a,b,ca,b,c be integers not divisible by pp. Prove that there are at most 1+2p1+\sqrt {2p} positive integers nn such that n<pn<p and pp divides an+bn+cna^n+b^n+c^n.
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