1. ## Prime factors

Hello!

I've got a little problem with the following assignment. I would be very grateful if anyone could at least give me some hint on how to do it.

There are given different odd prime numbers $p$ and $q$. Prove that number $2 ^ {pq} - 1$ has at least 3 different prime factors.

Thank you very much!

2. Originally Posted by PaulinaAnna
Hello!

I've got a little problem with the following assignment. I would be very grateful if anyone could at least give me some hint on how to do it.

There are given different odd prime numbers $p$ and $q$. Prove that number $2 ^ {pq} - 1$ has at least 3 different prime factors.

Thank you very much!
Maybe this?

Mersenne prime - Wikipedia, the free encyclopedia (subheading Generalization)

By the way I've marked this thread to be moved to the Number Theory subforum.

3. Let $\displaystyle m$ and $\displaystyle n$ be positive integers, if $\displaystyle m|n$, then $\displaystyle 2^m-1|2^n-1$.
Also, for any positive integers $\displaystyle m$ and $\displaystyle n$, if $\displaystyle (m,n)=1$, then $\displaystyle (2^n-1,2^m-1)=1$.

Apply these two lemmas in the same order they're written...

Hey!

Thank you guys very much.