Prove, that a composite number 2^p - 1 (where p is a prime) has at least 2 different prime factors.
How I tried to solve this problem:
I tried to write 2^p -1 as x^n (x, n are integers, n>1, just to prove that it can't be this way). I know that the only prime factors of 2^p - 1 can be numbers like 2kp+1 and I also tried this way. What is more, I tried with two cases- n odd and n even, separately. But I didn't manage to prove anything. Please, help. Thank you in advance.