An inductive proof of the Frobenius coin problem of two denominators

Giorgos Kapetanakis, Ioannis Rizos

Published 2023-08-06Version 1

Let $a,b$ be positive, relatively prime, integers. We prove, using induction, that for every $d > ab-a-b$ there exist $x,y\in\mathbb{Z}_{\geq 0}$, such that $d=ax+by$.