2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61921A 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.Number Theory11D09; 14M12; 11G05text