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 ?

Suppose that we have that some prime $p$ divides the gcd of ab and a+b. Then, we know that $p\mid a$ or $p\mid b$. WLOG suppose that p divides a. Then, it follows that a+b is divisible by by p, so b must also be divisible by p. But this means that $a$ and $b$ have a prime factor in common, contridicting the assumption that they were coprime.
