# Proof relating to prime numbers

• Jan 13th 2010, 10:02 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
• Jan 13th 2010, 10:15 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.
• Jan 13th 2010, 10:35 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
• Jan 13th 2010, 10:37 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 $\displaystyle p|ab$ we know that $\displaystyle ab=p\cdot p_1\cdots p_m$ and since $\displaystyle a$ and $\displaystyle b$ must be written as a product of those primes it follows that $\displaystyle p$ must be in one of them. That's roughly the cheat.
• Jan 13th 2010, 11:25 AM
rpatel
what does FTA stand for ?
• Jan 13th 2010, 11:26 AM
Drexel28
Quote:

Originally Posted by rpatel
what does FTA stand for ?

Fundamental theorem of arithmetic.
• Jan 13th 2010, 11:31 AM
rpatel
oh ok i haven't come accross FTA before.