If b>0 and a=bq + r, prove that (a,b) = (b,r)
I made an attempt... it didnt really go anywhere.
I think I can say that (a,b) = am + bn and (b,r) = bp + rq.
a = bq + r
b = rp + s
You can see that I have absolutely no idea how to solve this.
Any help would be greatly appreciated. Thank you in advance.