An Elementary Obstruction to the Existence of a Perfect Cuboid
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915785617702912 |
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| author | Yelle, Stéphane |
| author_facet | Yelle, Stéphane |
| contents | We study arithmetic constraints arising from the three faces meeting along the space diagonal of a rectangular cuboid. Using a propagation mechanism along this diagonal, based on the appearance of a minimal odd prime in certain triangular remainders, we derive strong structural restrictions on possible configurations. These constraints induce an infinite descent along the space diagonal, preventing the existence of a compatible integral structure. This approach provides an elementary obstruction to the existence of a perfect cuboid, relying only on divisibility and congruence arguments, and avoiding the use of Gaussian integers or classical quadratic factorizations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_00239 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Elementary Obstruction to the Existence of a Perfect Cuboid Yelle, Stéphane General Mathematics 11D41, 11A25 11D41, 11A25 We study arithmetic constraints arising from the three faces meeting along the space diagonal of a rectangular cuboid. Using a propagation mechanism along this diagonal, based on the appearance of a minimal odd prime in certain triangular remainders, we derive strong structural restrictions on possible configurations. These constraints induce an infinite descent along the space diagonal, preventing the existence of a compatible integral structure. This approach provides an elementary obstruction to the existence of a perfect cuboid, relying only on divisibility and congruence arguments, and avoiding the use of Gaussian integers or classical quadratic factorizations. |
| title | An Elementary Obstruction to the Existence of a Perfect Cuboid |
| topic | General Mathematics 11D41, 11A25 11D41, 11A25 |
| url | https://arxiv.org/abs/2602.00239 |