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 ?

First prove


*

*$\gcd(mn, k)=1$ if and only if $\gcd(m,k)=1$ and $\gcd(n,k)=1$.

*If $\gcd(m,k)=1$ then $\gcd(m,m+k)=1$.


The desired result follows from these like so: From $\gcd(a,b)=1$, we have $\gcd(a, a+b)=\gcd(b, a+b)=1$, implying 
$\gcd(ab, a+b)=1$.
