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Proof of a formula involving Euler's totient function.
I have this interesting question that I have difficulty to prove.
I know that:
$ \gcd(a,b) = d $
And I need tho show that:
$ \varphi(ab) = d\varphi(a)\varphi(b) / \varphi(d) $
where $\varphi$ is Euler's totient function