# Find All Integers Such that phi(n)=12

1. Mar 11, 2010

### cwatki14

I am trying to find all of the integers such that phi(n)=12. Clearly n=13 is one, but how do I do it for composite numbers?
-Thanks

2. Mar 11, 2010

### Tinyboss

What can you say about $$\varphi(a)\varphi(b)$$ with regard to $$\varphi(ab)$$? What about $$\varphi(p^n)$$ if p is prime?

3. Mar 11, 2010

### cwatki14

$$\varphi(a)\varphi(b)$$=$$\varphi(ab)$$ if (a,b)=1. $$\varphi(p^n)$$= $$\(p^n)$$-$$\(p^n-1)$$ if p is prime. So am I looking for all combinations of n in which the respective phi(n) add to equal 12? I.E. am I searching for prime factorizations of some n where these two properties will yield of phi of 12?