Naslov
On the existence of D(w)-quadruples in rings of integers of some number fields

Autori
Franušić, Zrinka

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
ALANT 3 — Joint Conferences on Algebra, Logic and Number Theory, Będlewo / - , 2014, 1-1

Skup
ALANT 3 — Joint Conferences on Algebra, Logic and Number Theory 10th Czech, Polish and Slovak Conference on Number Theory 15th Colloquiumfest on Algebra and Logic

Mjesto i datum
Będlewo, Poljska, 08.06.2014. - 13.06.2014

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Diophantine quadruple ; quadratic field ; pure cubic number field

Sažetak
Let R be a commutative ring with unity 1 and w∈R. The set of nonzero and distinct elements {; ; ; ; a_1, a_2, a_3, a_4}; ; ; ; in R such that a_ia_j + w is a perfect square in R for 1 ≤ i < j ≤ 4 is called a Diophantine quadruple with the property D(w) in R or just a D(w)- quadruple.The conjecture says that there exists a D(w)- quadruple if and only if w can be represented as a difference of two squares, up to finitely many exceptions. The aim of this talk is to show that the conjecture is correct for the ring of integers of the pure cubic number field Q((2)^(1/3)) and the imaginary quadratic field Q(√−3). represented as a difference of two squares, up to finitely many exceptions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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