Diophantine Quadruples and Cayley's Hyperdeterminant

Details Diophantine Quadruples and Cayley's Hyperdeterminant Diophantine Quadruples and Cayley's Hyperdeterminant

2001-07-28

arxiv.org/abs/math/0107203v2

Mathematics

Number Theory

Scientific paper

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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