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f(m)=f(2015) f(2016), f (x)=x^2 +px +q (HOMC 2016 S Q14)

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September 8, 2019
algebrapolynomialtrinomial

Problem Statement

Let f(x)=x2+px+qf (x) = x^2 + px + q, where p,qp, q are integers. Prove that there is an integer mm such that f(m)=f(2015)ā‹…f(2016)f (m) = f (2015) \cdot f (2016).
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