Problem

Source: Indian RMO 2013 Paper 1 Problem 6

Tags: quadratics, modular arithmetic, number theory, Diophantine equation, number theory unsolved



Suppose that $m$ and $n$ are integers, such that both the quadratic equations $x^2+mx-n=0$ and $x^2-mx+n=0$ have integer roots. Prove that $n$ is divisible by $6$.