$D(-1)$-triples of triangular numbers
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911556730617856 |
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| author | Trebješanin, Marija Bliznac |
| author_facet | Trebješanin, Marija Bliznac |
| contents | We study pairs and triples consisting of triangular numbers such that the product of any two distinct elements decreased by 1 is a perfect square. For a positive integer $n$, we establish a necessary condition for the $n$-th triangular number $T_n$ to be a member of such a pair, and we prove that any such $T_n$ is also a member of infinitely many $D(-1)$-triples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29565 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $D(-1)$-triples of triangular numbers Trebješanin, Marija Bliznac Number Theory 11B37, 11D09 We study pairs and triples consisting of triangular numbers such that the product of any two distinct elements decreased by 1 is a perfect square. For a positive integer $n$, we establish a necessary condition for the $n$-th triangular number $T_n$ to be a member of such a pair, and we prove that any such $T_n$ is also a member of infinitely many $D(-1)$-triples. |
| title | $D(-1)$-triples of triangular numbers |
| topic | Number Theory 11B37, 11D09 |
| url | https://arxiv.org/abs/2603.29565 |