Pregled bibliografske jedinice broj: 1124932
On the size of Diophantine m-tuples in imaginary quadratic number rings
On the size of Diophantine m-tuples in imaginary quadratic number rings // Bulletin of Mathematical Sciences, 11 (2021), 1; 1950020, 10 doi:10.1142/S1664360719500206 (međunarodna recenzija, članak, znanstveni)
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Naslov
On the size of Diophantine m-tuples in imaginary
quadratic number rings
Autori
Adžaga, Nikola
Izvornik
Bulletin of Mathematical Sciences (1664-3607) 11
(2021), 1;
1950020, 10
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Diophantine m-tuples ; Diophantine approximation ; Pell equations ; rings of integers ; Diophantine equations
Sažetak
A Diophantine m-tuple is a set of m distinct integers such that the product of any two distinct elements plus one is a perfect square. It was recently proven that there is no Diophantine quintuple in positive integers. We study the same problem in the rings of integers of imaginary quadratic fields. By using a gap principle proven by Diophantine approximations, we show that m≤42. Our proof is relatively simple compared to the proofs of similar results in positive integers.
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
Profili:
Nikola Adžaga
(autor)
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
