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arXiv · 2308.03050

An inductive proof of the Frobenius coin problem of two denominations

Giorgos Kapetanakis·Ioannis Rizos
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Abstract

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 $d=ax+by$. As a byproduct, we obtain a constructive recursive algorithm for identifying appropriate $x,y$ as above.

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Giorgos Kapetanakis, Ioannis Rizos. 2023-08-06. An inductive proof of the Frobenius coin problem of two denominations. https://arxiv.org/abs/2308.03050

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