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Perfect Square

Source: Switzerland Math Olympiad, Final round 2014, P2

June 2, 2014
number theoryleast common multiplenumber theory proposed

Problem Statement

Let a,b∈Na,b\in\mathbb{N} such that : ab(a−b)∣a3+b3+ab ab(a-b)\mid a^3+b^3+ab Then show that lcm⁡(a,b)\operatorname{lcm}(a,b) is a perfect square.
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