# Proof relating to prime numbers

• January 13th 2010, 11:02 AM
rpatel
Proof relating to prime numbers
Hi

I need help with this following proof. I can't seem to prove it. I believe there is something relating to coprime in this question.

I have attached my question as i didn't know all the various commands to type it in latex.

thanks
• January 13th 2010, 11:15 AM
Drexel28
Quote:

Originally Posted by rpatel
Hi

I need help with this following proof. I can't seem to prove it. I believe there is something relating to coprime in this question.

I have attached my question as i didn't know all the various commands to type it in latex.

thanks

What have you tried? I suppose you cannot use the FTA.
• January 13th 2010, 11:35 AM
Moo
Quote:

Originally Posted by Drexel28
What have you tried? I suppose you cannot use the FTA.

How would you use the FTA here ? (Surprised)

Well, the proof of the FTA uses methods that may be useful here :P

Edit : sorry, I've been constantly editing my message. This is the final version :D
• January 13th 2010, 11:37 AM
Drexel28
Quote:

Originally Posted by Moo
What's the relationship between his question and the fundamental theorem of algebra ? (Wondering)

Well, it's kind of cheating since you need this result to prove the FTA. Since $p|ab$ we know that $ab=p\cdot p_1\cdots p_m$ and since $a$ and $b$ must be written as a product of those primes it follows that $p$ must be in one of them. That's roughly the cheat.
• January 13th 2010, 12:25 PM
rpatel
what does FTA stand for ?
• January 13th 2010, 12:26 PM
Drexel28
Quote:

Originally Posted by rpatel
what does FTA stand for ?

Fundamental theorem of arithmetic.
• January 13th 2010, 12:31 PM
rpatel
oh ok i haven't come accross FTA before.