If $\gcd(a, b) = 1$ then $\gcd(ab, a+b) = 1$? In a mathematical demonstration, i saw:
If $\gcd(a, b) = 1$ Then $\gcd(ab, a+b) = 1$
I could not found a counter example, but i could not found a way to prove it too either.
Could you help me on this one ?

If a prime $p$ divides $ab$, then it divides $a$ or $b$. WLOG it divides $a$. If that prime also divides $a+b$, then since it divides $a$ it must divide $b$ as well, contradicting $gcd(a,b)=1$. 
