On an elementary method for solving $Ax^4-By^2=1$
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918374208962560 |
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| author | Walsh, P. G. |
| author_facet | Walsh, P. G. |
| contents | A new method for solving quartic equations due to Luo and Lin is investigated both computationally and theoretically. As a result, a completely straightforward elementary method is given for solving Bumby's equation $3X^4-2Y^2=1$, along with a conjecture, which if resolved, would enable a similar proof for a possibly infinite family of similar equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05809 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On an elementary method for solving $Ax^4-By^2=1$ Walsh, P. G. Number Theory 11D25 A new method for solving quartic equations due to Luo and Lin is investigated both computationally and theoretically. As a result, a completely straightforward elementary method is given for solving Bumby's equation $3X^4-2Y^2=1$, along with a conjecture, which if resolved, would enable a similar proof for a possibly infinite family of similar equations. |
| title | On an elementary method for solving $Ax^4-By^2=1$ |
| topic | Number Theory 11D25 |
| url | https://arxiv.org/abs/2603.05809 |