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?