Pregled bibliografske jedinice broj: 1114337
The Extension of the D(-k)-pair {;k,k+1}; to a Quadruple
The Extension of the D(-k)-pair {;k,k+1}; to a Quadruple // Periodica mathematica Hungarica, 85 (2022), 1; 148-163 doi:10.1007/s10998-021-00424-8 (međunarodna recenzija, članak, znanstveni)
CROSBI ID: 1114337 Za ispravke kontaktirajte CROSBI podršku putem web obrasca
Naslov
The Extension of the D(-k)-pair {;k,k+1}; to a
Quadruple
Autori
Adžaga, Nikola ; Filipin, Alan ; Fujita, Yasutsugu
Izvornik
Periodica mathematica Hungarica (0031-5303) 85
(2022), 1;
148-163
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Diophantine m-tuples ; Pellian equations ; hypergeometric method ; linear forms in logarithms
Sažetak
Let n be a non-zero integer. A set of m positive integers {; ; ; a_1, a_2, ... , a_m}; ; ; is called a D(n)- m-tuple if a_ia_j + n is a perfect square for all 1 <= i < j <= m. Let k be a positive integer. In this paper, we prove that if {; ; ; k, k+1, c, d}; ; ; is a D(-k)-quadruple with c>1, then d=1. The proof relies not only on standard methods in this field (Baker's linear forms in logarithms and hypergeometric method), but also on some less typical elementary arguments dealing with recurrences, as well as a relatively new method for determination of integral points on hyperelliptic curves.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
HRZZ-IP-2018-01-1313 - Diofantska geometrija i primjene (DIOPHANT) (Kazalicki, Matija, HRZZ - 2018-01) ( CroRIS)
Ustanove:
Građevinski fakultet, Zagreb
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
