Uniqueness theorem of generalized Markov numbers that are prime powers
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910521953878016 |
|---|---|
| author | Gyoda, Yasuaki Maruyama, Shuhei |
| author_facet | Gyoda, Yasuaki Maruyama, Shuhei |
| contents | In this paper, we study positive integer solutions to a generalized form of the Markov equation, given as $x^2 + y^2 + z^2 + k(yz + zx + xy) = (3 + 3k)xyz$. This equation extends the classical Markov equation $x^2 + y^2 + z^2 = 3xyz$. We generalize the concept of Cohn triples for the classical Markov equation to the generalized Markov equations. Using this, we provide a generalization of the uniqueness theorem of Markov numbers that are prime powers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07329 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniqueness theorem of generalized Markov numbers that are prime powers Gyoda, Yasuaki Maruyama, Shuhei Number Theory 11D25, 11J60 In this paper, we study positive integer solutions to a generalized form of the Markov equation, given as $x^2 + y^2 + z^2 + k(yz + zx + xy) = (3 + 3k)xyz$. This equation extends the classical Markov equation $x^2 + y^2 + z^2 = 3xyz$. We generalize the concept of Cohn triples for the classical Markov equation to the generalized Markov equations. Using this, we provide a generalization of the uniqueness theorem of Markov numbers that are prime powers. |
| title | Uniqueness theorem of generalized Markov numbers that are prime powers |
| topic | Number Theory 11D25, 11J60 |
| url | https://arxiv.org/abs/2312.07329 |