Original scientific paper
https://doi.org/10.21857/y26kecl809
Diophantine quintuples containing two pairs of conjugates in some quadratic fields
Zrinka Franušić
orcid.org/0000-0003-3481-8057
; Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia
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.
Keywords
Diophantine quintuples; regular Diophantine quadruples; quadratic fields
Hrčak ID:
283926
URI
Publication date:
27.9.2022.
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