Original scientific paper

https://doi.org/10.3336/gm.53.1.03

Strong Eulerian triples

Andrej Dujella orcid.org/0000-0001-6867-5811 ; Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
Ivica Gusić ; Faculty of Chemical Engineering and Technology , University of Zagreb , Marulićev trg 19, 10000 Zagreb, Croatia
Vinko Petričević ; Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
Petra Tadić ; Department of Economics and Tourism , Juraj Dobrila University of Pula , 52100 Pula, Croatia

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

Eulerian triples; elliptic curves

Hrčak ID:

201808

URI

https://hrcak.srce.hr/201808

Publication date:

20.6.2018.

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