A friend of mine posed this question: Assume three constants $a,b$ and $d$ and one variable x. $a,b$ & $d$ are all integers and $a$ and $b$ are coprime.$x$ can also be only an integer.
Now, is it possible to calculate $GCD(a*x-d*b,a-b*x)$ without having to do all the multiplications. In other words, is a simplification to this GCD expression possible?
I tried many things and have not managed to find if it is possible or not. Any clues or opinions are welcome.
Thanks