Strong Eulerian triples

Abstract

We prove that there exist infinitely many rationals a, b and c with the property that a^2-1, b^2-1, c^2-1, ab-1, ac-1 and bc-1 are all perfect squares. This provides a solution to a variant of the problem studied by Diophantus and Euler.

8 pages

References in corpus (3)

• More on Diophantine sextuples
• Triples which are $D(n)$-sets for several $n$'s
• Square Eulerian Quadruples

Cited by in corpus (2)

• Diophantine quadruples with the properties $D(n_1)$ and $D(n_2)$
• Strong rational Diophantine D(q)-triples