Problem

Source: Romanian 2018 TST Problem 2 Day 2

Tags: number theory, quadratic reciprocity, Sum of Squares, composite numbers



Show that a number $n(n+1)$ where $n$ is positive integer is the sum of 2 numbers $k(k+1)$ and $m(m+1)$ where $m$ and $k$ are positive integers if and only if the number $2n^2+2n+1$ is composite.