Glasnik Matematicki, Vol. 49, No. 1 (2014), 37-46.

ON D(W)-QUADRUPLES IN THE RINGS OF INTEGERS OF CERTAIN PURE NUMBER FIELDS

Ljerka Jukić Matić

Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, 31 000 Osijek, Croatia
e-mail: ljukic@mathos.hr


Abstract.   The purpose of this paper is to show the non-existence of D(w)-quadruples in number fields of odd degree whose rings of integers are of the special form. We derive some elements which can not be represented as difference of squares in such rings and comment the non-existence of corresponding Diophantine quadruples. This relies on the non-solvability of system of congruences which we prove in some low-degree cases.

2010 Mathematics Subject Classification.   11D09, 11R16, 11D79.

Key words and phrases.   Diophantine quadruples, pure number fields, cyclic bases.


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DOI: 10.3336/gm.49.1.04


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