Problem

Source: 2012cmo,problem5

Tags: modular arithmetic, inequalities, number theory proposed, number theory



Consider a square-free even integer n and a prime p, such that 1) (n,p)=1; 2) p2n; 3) There exists an integer k such that p|n+k2. Prove that there exists pairwise distinct positive integers a,b,c such that n=ab+bc+ca. Proposed by Hongbing Yu