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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.24650 |
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| _version_ | 1866918470157860864 |
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| author | Fuchs, Clemens Schönauer, Miriam |
| author_facet | Fuchs, Clemens Schönauer, Miriam |
| contents | In this paper, we prove that there are no $k$-th power Diophantine triples of the form $\{a^k,b,c\}$ for $k\geq 3$ and $1<a^k<b<c$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24650 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On $k$-th power Diophantine triples of the form $\{a^k, b, c\}$ Fuchs, Clemens Schönauer, Miriam Number Theory 11D41, 11D45, 11J68 In this paper, we prove that there are no $k$-th power Diophantine triples of the form $\{a^k,b,c\}$ for $k\geq 3$ and $1<a^k<b<c$. |
| title | On $k$-th power Diophantine triples of the form $\{a^k, b, c\}$ |
| topic | Number Theory 11D41, 11D45, 11J68 |
| url | https://arxiv.org/abs/2604.24650 |