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Found problems: 1

2005 Federal Math Competition of S&M, Problem 1
Tags: power mean , divisibility , algebra , number theory
Let $a$ and $b$ be positive integers and $K=\sqrt{\frac{a^2+b^2}2}$, $A=\frac{a+b}2$. If $\frac KA$ is a positive integer, prove that $a=b$.