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Mathematical Communications, Vol. 9 No. 2, 2004.

Original scientific paper

Diophantine quadruples in the ring Z[√2]

Z. Franušić

Full text: english pdf 119 Kb

page 141-148

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Abstract

The set of integers of the quadratic field Q(√d)has the property D(z) if the product of its any two distinct elements increased by z is a perfct square in Q(√d). In case d=2, we prove that there exist infinitely many integer quadruples with the property D(z) if and only if z can be represented as a difference of two squares of integers in Q(√2).

Keywords

Diophantine quadruples; difference of squares; quadratic fields; Pellian equations

Hrčak ID:

680

URI

https://hrcak.srce.hr/680

Publication date:

22.12.2004.

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