Problem

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Tags: number theory, Euler s totient function



Determine all the pairs of positive odd integers $(a,b),$ such that $a,b>1$ and $$7\varphi^2(a)-\varphi(ab)+11\varphi^2(b)=2(a^2+b^2),$$where $\varphi(n)$ is Euler's totient function.