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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2604.26183 |
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| _version_ | 1866914515122126848 |
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| author | Das, Shamik Mondal, Sudipa |
| author_facet | Das, Shamik Mondal, Sudipa |
| contents | In this article, we produce infinite families of non-congruent numbers in the residue class of $1,2,$ and $3$ modulo $8$ with arbitrarily many triples or quadruples prime factors. In short, we use Monsky matrix to show that the $2$-Selmer rank of the corresponding congruent number elliptic curve is zero. We also establish some quantitative results to conclude that each such family contains infinitely many non-congruent numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26183 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monsky Matrix and 2-Selmer rank Das, Shamik Mondal, Sudipa Number Theory 11G05, 11C20, 15A24, 15A09, 11A15 In this article, we produce infinite families of non-congruent numbers in the residue class of $1,2,$ and $3$ modulo $8$ with arbitrarily many triples or quadruples prime factors. In short, we use Monsky matrix to show that the $2$-Selmer rank of the corresponding congruent number elliptic curve is zero. We also establish some quantitative results to conclude that each such family contains infinitely many non-congruent numbers. |
| title | Monsky Matrix and 2-Selmer rank |
| topic | Number Theory 11G05, 11C20, 15A24, 15A09, 11A15 |
| url | https://arxiv.org/abs/2604.26183 |