engleski

Diophantine quadruples in Z[√ -2]

We study the existence of Diophantine quadruples with the property D(z) in the ring Z[√ -2]. We find several new polynomial formulas for Diophantine quadruples with the property D(a+b√ -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 characterize elements z of Z[√ -2] for which a Diophantine quadruple with the property D(z) exists.

diophantine quadruples; quadratic field

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