engleski

Diophantine quadruples in Z[√ -2]

In this paper, we study the existence of Diophantine quadruples with the property D(z) in the ring Z[sqrt(-2)]. We find several new polynomial formulas for Diophantine quadruples with the property D(a+b*sqrt(-2)), for integers a and b satisfying certain congruence conditions. These formulas, together with previous results on this subject by Abu Muriefah, Al-Rashed and Franusic, allow us to almost completely char- acterize elements z of Z[sqrt(-2)] for which a Diophantine quadruple with the property D(z) exists.

Diophantine quadruples ; quadratic field

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