An inductive proof of the Frobenius coin problem of two denominations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908420181852160 |
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| author | Kapetanakis, Giorgos Rizos, Ioannis |
| author_facet | Kapetanakis, Giorgos Rizos, Ioannis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03050 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An inductive proof of the Frobenius coin problem of two denominations Kapetanakis, Giorgos Rizos, Ioannis Number Theory 11D07 (Primary) 11D04 (Secondary) 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. |
| title | An inductive proof of the Frobenius coin problem of two denominations |
| topic | Number Theory 11D07 (Primary) 11D04 (Secondary) |
| url | https://arxiv.org/abs/2308.03050 |