So if m and n are relatively prime, then the $\phi(mn)=\phi(m)*\phi(n)$ but what happens when $d > 1$?
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Semsem
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terminix00
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http://math.stackexchange.com/questions/114841/proofofaformulainvolvingeulerstotientfunction – lab bhattacharjee Apr 15 '14 at 04:28
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Denote $P$ as the product of primes common to $m$ and $n$. Then $\phi(mn) = P \phi(m) \phi(n)/\phi(P)$ which generalizes all of this. Found in Niven's book and easy to prove by writing out the factorization of $m,n$.
Sandeep Silwal
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