Rad HAZU, Matematičke znanosti, Vol. 18 (2014), 15-25.

THE PROBLEM OF DIOPHANTUS FOR INTEGERS OF Q(√-3)

Zrinka Franušić and Ivan Soldo

Department of Mathematics, University of Zagreb, Bijenička cesta 30, HR-10 000 Zagreb, Croatia
e-mail: fran@math.hr

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

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.

2010 Mathematics Subject Classification.   11D09, 11R11.

Key words and phrases.   Diophantine quadruples, quadratic field.

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