We just had about the greatest common divisor, gcd(a,b). We've seen the proof, and now we have to prove that the gcd(a,b) = gcd(a,b-ax). I'm sitting here have troubles even starting the problem. It also says that a,b,x is in Z. I see that if x is 0, then it says that gcd(a,b) = gcd(a,b) which is of course true. And it also seems that the highest x can be is the gcd(a,b), since if it goes any higher than the greatest common divisor, that will of course be the greater common divisor. I'm not really sure how to even start this problem, and am I supposed to prove it always works, since couldn't I just say that x always have to be 0? Or do I need to prove that it works for all the numbers from 0 up to the gcd(a,b) or am I misunderstanding the problem completely? It would be nice if anyone could just give me some ideas to start it off, I would be very grateful.