Problem

Source: ELMO 2013/5, by Andre Arslan; also Shortlist N2

Tags: algebra, polynomial, geometry, 3D geometry, modular arithmetic, number theory, hehecombinatoricstoo



For what polynomials P(n) with integer coefficients can a positive integer be assigned to every lattice point in R3 so that for every integer n1, the sum of the n3 integers assigned to any n×n×n grid of lattice points is divisible by P(n)? Proposed by Andre Arslan