A Quartic Identity Related to Fermat-Type Equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2014
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| _version_ | 1866918324780138496 |
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| author | Winkler, Mike Fillipi, Andreas |
| author_facet | Winkler, Mike Fillipi, Andreas |
| contents | We provide a short proof of an algebraic identity. For integers $n\ge 2$ and variables $x,y,z$, it represents $(x^n+y^n-z^n)$ as a value of the quadratic form $\mathcal A^2+\mathcal B^2-\mathcal C^2$ after multiplication by an explicit factor. Consequently, any hypothetical solution of $x^n+y^n=z^n$ yields a Pythagorean triple $(\mathcal A,\mathcal B,\mathcal C)$ consisting of explicit polynomial expressions in $x,y,z$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1412_1689 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | A Quartic Identity Related to Fermat-Type Equations Winkler, Mike Fillipi, Andreas General Mathematics We provide a short proof of an algebraic identity. For integers $n\ge 2$ and variables $x,y,z$, it represents $(x^n+y^n-z^n)$ as a value of the quadratic form $\mathcal A^2+\mathcal B^2-\mathcal C^2$ after multiplication by an explicit factor. Consequently, any hypothetical solution of $x^n+y^n=z^n$ yields a Pythagorean triple $(\mathcal A,\mathcal B,\mathcal C)$ consisting of explicit polynomial expressions in $x,y,z$. |
| title | A Quartic Identity Related to Fermat-Type Equations |
| topic | General Mathematics |
| url | https://arxiv.org/abs/1412.1689 |