Prove:

For all pos. integers , if sum of divisors of is , then is prime.

Apparently this is famous. This is an intro course though and the proofs I found tend to be complicated. Prove it by contrapositive? Or contradiction?

Anyone know how to prove it?

The proof I found is: the sum of divisors is at least since and divide . If it's , we then know there are no other divisors. Thus, is prime.

How do we know there are no other divisors?