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Found problems: 1

2023 Brazil Cono Sur TST, 3
Tags: p-adic valuation
Let $a,b,c$ be positive integers satisfying $\gcd(a,b,c)=1$ and $$\dfrac{ab}{c}+\dfrac{bc}{a}+\dfrac{ca}{b}$$ is an integer. Prove that $abc$ is a perfect square.