Hello and thanks for looking
I have to prove the following :Prove that gcd(a,b) = 1 if and only if gcd(ab,a+b)=1
Thanks a lot in advance for the help
Hello,
Proving this implication : $\displaystyle gcd(ab,a+b)=1 \implies gcd(a,b)=1$
Let $\displaystyle d=gcd(a,b)$
d divides a and d divides b. Therefore, d (and even d˛) divides ab and d divides (a+b).
But we know that gcd(ab,a+b)=1.
--> d divides 1.
So d=1.