English

Strong Eulerian triples

Number Theory 2018-07-03 v1

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.

Keywords

Cite

@article{arxiv.1802.00291,
  title  = {Strong Eulerian triples},
  author = {Andrej Dujella and Ivica Gusić and Vinko Petričević and Petra Tadić},
  journal= {arXiv preprint arXiv:1802.00291},
  year   = {2018}
}

Comments

8 pages

R2 v1 2026-06-23T00:07:31.238Z