Frobenius numbers associated with Diophantine triples of $x^2+y^2=z^r$ (extended version)
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911793639587840 |
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| author | Komatsu, Takao Gupta, Neha Upreti, Manoj |
| author_facet | Komatsu, Takao Gupta, Neha Upreti, Manoj |
| contents | We give an explicit formula for the $p$-Frobenius number of triples associated with Diophantine equations $x^2+y^2=z^r$, that is, the largest positive integer that can only be represented in $p$ ways by combining the three integers of the solutions of Diophantine equations $x^2+y^2=z^r$. When $r=2$, the Frobenius number has already been given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07534 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Frobenius numbers associated with Diophantine triples of $x^2+y^2=z^r$ (extended version) Komatsu, Takao Gupta, Neha Upreti, Manoj Number Theory Combinatorics We give an explicit formula for the $p$-Frobenius number of triples associated with Diophantine equations $x^2+y^2=z^r$, that is, the largest positive integer that can only be represented in $p$ ways by combining the three integers of the solutions of Diophantine equations $x^2+y^2=z^r$. When $r=2$, the Frobenius number has already been given. |
| title | Frobenius numbers associated with Diophantine triples of $x^2+y^2=z^r$ (extended version) |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2403.07534 |