Pregled bibliografske jedinice broj: 983293
A polynomial variant of a problem of Diophantus and its consequences
A polynomial variant of a problem of Diophantus and its consequences // Glasnik matematički, 54 (2019), 1; 21-52 doi:10.3336/gm.54.1.03 (međunarodna recenzija, članak, znanstveni)
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Naslov
A polynomial variant of a problem of Diophantus
and its consequences
Autori
Filipin, Alan ; Jurasić, Ana
Izvornik
Glasnik matematički (0017-095X) 54
(2019), 1;
21-52
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Diophantine m-tuples ; polynomials
Sažetak
In this paper we prove that every Diophantine quadruple in R[X] is regular. In other words, we prove that if {; ; ; ; a, b, c, d}; ; ; ; is a set of four non-zero elements of R[X], not all constant, such that the product of any two of its distinct elements increased by 1 is a square of an element of R[X], then (a+b−c−d)^2=4(ab+1)(cd+1). Some consequences of the above result are that for an arbitrary n ∈N there does not exist a set of five non-zero elements from Z[X], which are not all constant, such that the product of any two of its distinct elements increased by n is a square of an element of Z[X]. Furthermore, there can exist such a set of four non-zero elements of Z[X] if and only if n is a square.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
HRZZ-IP-2013-11-6422 - Diofantove m-torke, eliptičke krivulje, Thueove i indeksne jednadžbe (DIOPHANTINE) (Dujella, Andrej, HRZZ - 2013-11) ( CroRIS)
Ustanove:
Građevinski fakultet, Zagreb,
Sveučilište u Rijeci, Fakultet za matematiku
Citiraj ovu publikaciju:
Časopis indeksira:
- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
Uključenost u ostale bibliografske baze podataka::
- MathSciNet
- Zentrallblatt für Mathematik/Mathematical Abstracts