# Prime factors

• Sep 6th 2010, 09:48 AM
PaulinaAnna
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 http://www.mymathforum.com/cgi-bin/mimetex.cgi?p and http://www.mymathforum.com/cgi-bin/mimetex.cgi?q. Prove that number http://www.mymathforum.com/cgi-bin/m...Bpq%7D%20-%201 has at least 3 different prime factors.

Thank you very much!
• Sep 6th 2010, 11:55 AM
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Quote:

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 http://www.mymathforum.com/cgi-bin/mimetex.cgi?p and http://www.mymathforum.com/cgi-bin/mimetex.cgi?q. Prove that number http://www.mymathforum.com/cgi-bin/m...Bpq%7D%20-%201 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.
• Sep 6th 2010, 02:53 PM
melese
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...
• Sep 7th 2010, 05:28 AM
PaulinaAnna
Hey!

Thank you guys very much.