True or false (and of course why):

Euler's totient function implies all its range for odd variables.

I proved that for all n>1 odd numbers:

φ(n)=φ(2n).

But it's not enough. Because I should prove that for all even n I can find an odd k for which:

φ(n)=φ(2k). But I can't see it.

Please help me!

Any help would be appreciated.

Thanks!