Show that if a ≥ b > 0, and gcd(a,b)=d, and as+bt=d, then the values s and t satisfy: |s| ≤ b/d and |t| ≤ a/d Hint: prove by induction on b: be careful, you have to stop the induction before b gets to zero, so the last step to consider is when b | a.
I think the base case is b=1, but I can't seem to find how to even show that this is true for b=1.
Also, in the hint: "the last step to consider is when b | a"- why not just "when b=1"?