MathDB
Prime dividing values of a polynomial!

Source: India TST 2001 Day 2 Problem 2

January 31, 2015
algebrapolynomialnumber theory unsolvednumber theory

Problem Statement

Let Q(x)Q(x) be a cubic polynomial with integer coefficients. Suppose that a prime pp divides Q(xj)Q(x_j) for j=1j = 1 ,22 ,33 ,44 , where x1,x2,x3,x4x_1 , x_2 , x_3 , x_4 are distinct integers from the set {0,1,⋯ ,p−1}\{0,1,\cdots, p-1\}. Prove that pp divides all the coefficients of Q(x)Q(x).
Back to ProblemsView on AoPS