Let $a$ and $b$ be positive integers such that $2a^2 + a = 3b^2 + b$. Prove that $a-b$ is a perfect square.
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Tags: number theory, diophantine
Let $a$ and $b$ be positive integers such that $2a^2 + a = 3b^2 + b$. Prove that $a-b$ is a perfect square.