For what integers does phi(n) | n and why?
Let be a prime and a positive integer, .
So you see that the only prime such that is .
Let be an integer such that , and its unique decomposition in a product of primes, with and . Then, for all has to divide , and a consequence is .
so , and since is odd, that means .
If , that's ok; if , and can't divide and
As you may see, .
Furthermore, .
Conclusion: the integers such that are the elements of