I need some help on how to prove this statement. I don't know where to start!

Prove that if d and n are positive integers such that d|n, then φ(dn) = dφ(n).

A lot of help is appreciated.. I tried writing

and where through are the same for both and .

But I don't know where to go from there....

Thanks

2. Originally Posted by kapowiee

I need some help on how to prove this statement. I don't know where to start!

Prove that if d and n are positive integers such that d|n, then φ(dn) = dφ(n).

A lot of help is appreciated.. I tried writing

and where through are the same for both and .

But I don't know where to go from there....

Thanks

Perhaps recalling that $n=p^{a_1}_1\cdot \ldots \cdot p^{a_r}_r \Longrightarrow$ $\phi(n)=n\prod\limits_{k=1}^r\left(1-\frac{1}{p_k}\right)$ could help a lot...

Tonio