Formulas for Diophantine quintuples containing two pairs of conjugates in some quadratic fields (CROSBI ID 284584)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Dujella, Andrej ; Franušić, Zrinka ; Petričević, Vinko
engleski
Formulas for Diophantine quintuples containing two pairs of conjugates in some quadratic fields
Let D be a positive integer which is not a perfect square. We consider Diophantine quintuples in the ring Z[√D] of the form {; ; e, a ± b√D, c ± d√D}; ; where a, b, c, d, e are integers. In this paper, we show that there exists a Diophantine quintuple of that form for certain values of D, including D = 1 + n^2(n + 1)^2 and some other polynomials of degree 4, and we represent its elements also as polynomials in n.
Diophantine quintuples, regular Diophantine quadruples, quadratic fields
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Podaci o izdanju
85 (2)
2022.
301-313
objavljeno
0031-5303
1588-2829
10.1007/s10998-021-00436-4