Diophantine Quadruples and Cayley's Hyperdeterminant
Number Theory
2007-05-23 v2
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.
Cite
@article{arxiv.math/0107203,
title = {Diophantine Quadruples and Cayley's Hyperdeterminant},
author = {Philip Gibbs},
journal= {arXiv preprint arXiv:math/0107203},
year = {2007}
}