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Possible Duplicate:
Proof of a formula involving Euler's totient function.

For positive integers $m$ and $n$ where $d=gcd(m,n)$, show that $$\phi(mn) = \phi(m)\phi(n)\frac{d}{\phi(d)}$$

This is just the generalization of the multiplicative property of phi function.I have tried to solve this in the same way as the proof of multiplicative property but couldn't get far.Please help.

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    You can find som proofs in this question (and in the questions linked to it): [Proof of a formula involving Euler's totient function.](http://math.stackexchange.com/questions/114841/proof-of-a-formula-involving-eulers-totient-function)2012-06-17
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    See also http://math.stackexchange.com/questions/119911/proving-formula-involving-eulers-totient-function2012-06-17

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