Problem

Source: Indonesia Mathematical Olympiad (INAMO) 2019 Problem 01

Tags: number theory, primes



Given that $n$ and $r$ are positive integers. Suppose that \[ 1 + 2 + \dots + (n - 1) = (n + 1) + (n + 2) + \dots + (n + r) \]Prove that $n$ is a composite number.