Positive integers $a, b$ satisfy equality $b^2 = a^2 + ab + b$. Prove that $b$ is a square of a positive integer. (Patrik Bak)
Source: 2020 Czech and Slovak Olympiad III A p4
Tags: number theory, Perfect Square
Positive integers $a, b$ satisfy equality $b^2 = a^2 + ab + b$. Prove that $b$ is a square of a positive integer. (Patrik Bak)