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Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, No. 519=18, 2014.

Original scientific paper

The problem of Diophantus for integers of Q(√−3)

Zrinka Franušić orcid id orcid.org/0000-0003-3481-8057 ; Department of Mathematics, University of Zagreb, Bijenička cesta 30, HR-10 000 Zagreb, Croatia
Ivan Soldo orcid id orcid.org/0000-0002-6195-6626 ; Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, HR-31 000 Osijek, Croatia

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Abstract

We solve the problem of Diophantus for integers of the
quadratic field Q(√−3) by finding a D(z)-quadruple in Z[(1+√−3)/2] for
each z that can be represented as a difference of two squares of integers in Q(√−3), up to finitely many possible exceptions.

Keywords

Diophantine quadruples; quadratic field

Hrčak ID:

127639

URI

https://hrcak.srce.hr/127639

Publication date:

30.9.2014.

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