Rad HAZU, Matematičke znanosti, Vol. 26 (2022), 45-53.

DIOPHANTINE QUINTUPLES CONTAINING TWO PAIRS OF CONJUGATES IN SOME QUADRATIC FIELDS

Zrinka Franušić

Abstract.   In this paper, we describe constructions of Diophantine quintuples of the special form in rings Z[√D] for certain positive integer D. The term "special form" refers to Diophantine quintuples of the form {e, a + b√D, a - b√D, c + d√D, c - d√D}, where a, b, c, d, e are integers. Also, we assume these quintuples contain two regular Diophantine quadruples.

2020 Mathematics Subject Classification.   11D09, 11R11.

Key words and phrases.   Diophantine quintuples, regular Diophantine quadruples, quadratic fields.

DOI: https://doi.org/10.21857/y26kecl809

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