Diophantine Quadruples and Cayley's Hyperdeterminant

Philip Gibbs

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Diophantine Quadruples and Cayley's Hyperdeterminant

Philip Gibbs

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Abstract

A famous problem posed by Diophantus was to find sets of distinct positive rational numbers such that the product of any two is one less than a rational square. Such Diophantine sets have been used to construct high rank elliptic curves. Here I demonstrate a link with Cayley's hyperdeterminants which provides a fruitful generalisation of Diophantine quadruples.

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Philip Gibbs. 2001-09-09. Diophantine Quadruples and Cayley's Hyperdeterminant. https://arxiv.org/abs/math/0107203

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