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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2604.17018 |
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| _version_ | 1866917451901435904 |
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| author | Andrašek, Alen |
| author_facet | Andrašek, Alen |
| contents | A rational Diophantine $m$-tuple is a set $\{a_1,\ldots,a_m\}$ of distinct nonzero rational numbers such that $a_i a_j+1$ is a square for all $1\leq i < j\leq m$. Similarly, we may ask when $a_ia_j+1$ is a $k$-th power. Here, we study the case $k=4$ and produce some non-trivial infinite families of such triples. We show that there are infinitely many triples with positive elements for $k=4$. We also briefly consider the $k=6$ (sextic) and $k=8$ (octic) cases, explaining the difficulties in extending the method to higher exponents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17018 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Regular Higher Power Rational Diophantine Triples Andrašek, Alen Number Theory A rational Diophantine $m$-tuple is a set $\{a_1,\ldots,a_m\}$ of distinct nonzero rational numbers such that $a_i a_j+1$ is a square for all $1\leq i < j\leq m$. Similarly, we may ask when $a_ia_j+1$ is a $k$-th power. Here, we study the case $k=4$ and produce some non-trivial infinite families of such triples. We show that there are infinitely many triples with positive elements for $k=4$. We also briefly consider the $k=6$ (sextic) and $k=8$ (octic) cases, explaining the difficulties in extending the method to higher exponents. |
| title | On Regular Higher Power Rational Diophantine Triples |
| topic | Number Theory |
| url | https://arxiv.org/abs/2604.17018 |