MathDB

1

Part of 2013 Poland - Second Round

Problems(1)

Divisibility of product, trinomial

Source: 64 Polish MO 2013 Second Round - Problem 1

4/21/2018
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.
trinomialDivisibilitynumber theoryPoland