Suppose that n is a positive integer with E(n) = 8 .. E denotes Euler Phi Function

Show that if p is an odd prime divisor of n, then p=3 or 5

and hence find all possible values for n?

To be honest, I did this more intuitively, then systematically.. I arrive at the solution fo 15. Which makes sense, since p|15 .... and give me E(15) = 8

How would I approach this question in a more formal fashion ?

Thanks