MathDB
Divisibility of product, trinomial

Source: 64 Polish MO 2013 Second Round - Problem 1

April 21, 2018
trinomialDivisibilitynumber theoryPoland

Problem Statement

Let bb, cc be integers and f(x)=x2+bx+cf(x) = x^2 + bx + c be a trinomial. Prove, that if for integers k1k_1, k2k_2 and k3k_3 values of f(k1)f(k_1), f(k2)f(k_2) and f(k3)f(k_3) are divisible by integer n≠0n \neq 0, then product (k1−k2)(k2−k3)(k3−k1)(k_1 - k_2)(k_2 - k_3)(k_3 - k_1) is divisible by nn too.
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