Thread: i tried working this question and i reached to a certain point. i really need help

Let a,b is an element of Z. prove that for all x is an element of Z we have gdc(a,b)= gcd(a,b-xa)

i meant gcd**

The pairs (a, b) and (a, b - xa) have not only the same greatest common divisor, but the same set of common divisors.