Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Update: I think there was a typo in the text. Please don't waste your time with this problem. :)

If gcd$(a,b) = p$, a prime, then $p|am$ and $p|an$ such that gcd$(m,n) = 1$

Why does gcd$(m,n)$ have to be equal to 1? And does this statement hold true if gcd$(a,b)$ is not equal to a prime?

share|improve this question

2 Answers 2

It doesn't. I think something has been misread.

Let $a=7$ and $b=14$, then $\gcd(a,b) = 7$ which is prime. Obviously $7|7m$ and $7|7n$ for any positive integers $m$ and $n$. Let $m = 2$ and $n = 4$ then $7|7\times 2$ and $7|7\times 4$, yet $\gcd(2,4) = 2 \neq 1$.

share|improve this answer

Your original statement seems like it is miscopied from somewhere, or missing additional context. If $\gcd(a,b)=p$, prime or not, then $a=pc$ and $b=pd$, for some integers $c,d$ such that $\gcd(c,d)=1$.

share|improve this answer
    
The other answer points out that if you don't have some sort of conditions on $m,n$ the original statement is incorrect. You will note that both answers suggest this possibility. –  vadim123 May 11 '13 at 23:10

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.