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arXiv · 1205.3135

Perfect cuboids and multisymmetric polynomials

Ruslan Sharipov
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Abstract

A perfect Euler cuboid is a rectangular parallelepiped with integer edges and integer face diagonals whose space diagonal is also integer. The problem of finding such parallelepipeds or proving their non-existence is an old unsolved mathematical problem. The Diophantine equations of a perfect Euler cuboid have an explicit $S_3$ symmetry. In this paper the cuboid equations are factorized with respect to their $S_3$ symmetry in terms of multisymmetric polynomials. Some factor equations are calculated explicitly.

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Ruslan Sharipov. 2012-05-14. Perfect cuboids and multisymmetric polynomials. https://arxiv.org/abs/1205.3135

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