Infinite families of rational Diophantine triples exist where each pairwise product plus one is a fourth power, including all-positive families.
Diagonal genus 5 curves, elliptic curves overQ(t), and rational diophantine quintuples
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On Regular Higher Power Rational Diophantine Triples
Infinite families of rational Diophantine triples exist where each pairwise product plus one is a fourth power, including all-positive families.