Glasnik Matematicki, Vol. 53, No. 1 (2018), 33-42.

STRONG EULERIAN TRIPLES

Andrej Dujella, Ivica Gusić, Vinko Petričević and Petra Tadić

Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
e-mail: duje@math.hr

Faculty of Chemical Engineering and Technology , University of Zagreb , Marulićev trg 19, 10000 Zagreb, Croatia
e-mail: igusic@fkit.hr

Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
e-mail: vpetrice@math.hr

Department of Economics and Tourism , Juraj Dobrila University of Pula , 52100 Pula, Croatia
e-mail: ptadic@unipu.hr


Abstract.   We prove that there exist infinitely many rationals a, b and c with the property that a2-1, b2-1, c2-1, 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.

2010 Mathematics Subject Classification.   11D09, 11G05.

Key words and phrases.   Eulerian triples, elliptic curves.


Full text (PDF) (access from subscribing institutions only)

DOI: 10.3336/gm.53.1.03


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