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Found problems: 1

2019 Canada National Olympiad, 2
Tags: number theory , cube of a natural number.
Let $a,b$ be positive integers such that $a+b^3$ is divisible by $a^2+3ab+3b^2-1$. Prove that $a^2+3ab+3b^2-1$ is divisible by the cube of an integer greater than 1.