3

Part of 2008 IberoAmerican

Problems(1)

P(x) - P(y) divisible by 107

Source: Iberoamerican Olympiad 2008, problem 3

Let P(x) \equal{} x^3 \plus{} mx \plus{} n be an integer polynomial satisfying that if P(x) \minus{} P(y) is divisible by 107, then x \minus{} y is divisible by 107 as well, where

x

y

are integers. Prove that 107 divides

m

algebrapolynomialquadraticsnumber theory proposednumber theory