engleski

The problem of existence of Diophantine quadruples in Z[√ -2]

We study the existence of Diophantine quadruples with the property D(z) in the ring Z[√ -2]. We significantly extended the results of Abu Muriefah and Al-Rashed and obtain several new formulas for Diophantine quadruples with the property D(a+b√ -2), for integers a and b satisfying certain congruence conditions. In that way, we solved the problem of existence of D(z)-quadruples of a large class of elements z of the ring Z[√ -2].

diophantine quadruples; quadratic field

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