Glasnik matematički, Vol. 53 No. 1, 2018.
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
Publication date:
20.6.2018.
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