Pregled bibliografske jedinice broj: 1280085
Extensions of a Diophantine triple by adjoining smaller elements II
Extensions of a Diophantine triple by adjoining smaller elements II // Periodica mathematica Hungarica (2023) (znanstveni, prihvaćen)
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Naslov
Extensions of a Diophantine triple by adjoining
smaller elements II
Autori
Cipu, Mihai ; Dujella, Andrej ; Fujita, Yasutsugu
Vrsta, podvrsta
Radovi u časopisima,
znanstveni
Izvornik
Periodica mathematica Hungarica (2023)
Status rada
Prihvaćen
Ključne riječi
Diophantine m-tuples, Pellian equations
Sažetak
Let {;a 1 , b, c}; and {;a 2 , b, c}; be Diophantine triples with a 1 < b < a 2 < c and a 2 ̸ = b + c − 2 √ bc + 1. Put d 2 = a 2 + b + c + 2a 2 bc − 2r 2 st, where r 2 = √ a 2 b + 1, s = √ ac + 1 and t = √ bc + 1. In this paper, we prove that if c ≤ 16µ 2 b 3 , where µ = min{;a 1 , d 2 };, then {;a 1 , a 2 , b, c}; is a Diophantine quadruple. Combining this result with one of our previous results implies that if {;a i , b, c, d}; (i ∈ {;1, 2, 3};) are Diophantine quadruples with a 1 < a 2 < b < a 3 < c < d, then a 3 = b + c − 2 √ bc + 1. It immediately follows that there does not exist a septuple {;a 1 , a 2 , a 3 , a 4 , b, c, d}; with a 1 < a 2 < b < a 3 < a 4 < c < d such that {;a i , b, c, d}; (i ∈ {;1, 2, 3, 4};) are Diophantine quadruples. Moreover, it is shown that there are only finitely many sextuples {;a 1 , a 2 , a 3 , b, c, d}; with a 1 < b < a 2 < a 3 < c < d such that {;a i , b, c, d}; (i ∈ {;1, 2, 3};) are Diophantine quadruples.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
--KK.01.1.1.01.0004 - Provedba vrhunskih istraživanja u sklopu Znanstvenog centra izvrsnosti za kvantne i kompleksne sustave te reprezentacije Liejevih algebri (QuantiXLie) (Buljan, Hrvoje; Pandžić, Pavle) ( CroRIS)
HRZZ-IP-2018-01-1313 - Diofantska geometrija i primjene (DIOPHANT) (Kazalicki, Matija, HRZZ - 2018-01) ( CroRIS)
Ustanove:
Prirodoslovno-matematički fakultet, Zagreb
Profili:
Andrej Dujella
(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