As a consequence of Bezout's identity, if a and b are coprime there exist integers x and y such that: ax + by = 1 The extension states that, if a and b are coprime the least natural number k for which all natural numbers greater than k can be expressed in the form: ax + by Is a+b-1. (Where x and y are natural numbers) I am trying to prove this extension. I have used C++ to test it for a few specific examples, but this does not cut the mustard. I need a rigorous proof. I looked up ideals and ring theory, but I am at a loss because I am doing a physics and applied maths degree, I have very little knowledge of pure mathematics. Any help would be greatly appreciated, thanks in advance.