Infinite families of rational Diophantine triples exist where each pairwise product plus one is a fourth power, including all-positive families.
On the quartic surfacex 4 +y 4 =z 4 +w 4
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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.