Pretražite po imenu i prezimenu autora, mentora, urednika, prevoditelja

Napredna pretraga

Pregled bibliografske jedinice broj: 1280085

Extensions of a Diophantine triple by adjoining smaller elements II


Cipu, Mihai; Dujella, Andrej; Fujita, Yasutsugu
Extensions of a Diophantine triple by adjoining smaller elements II // Periodica mathematica Hungarica (2023) (znanstveni, prihvaćen)


CROSBI ID: 1280085 Za ispravke kontaktirajte CROSBI podršku putem web obrasca

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:

Avatar Url Andrej Dujella (autor)

Poveznice na cjeloviti tekst rada:

Pristup cjelovitom tekstu rada

Citiraj ovu publikaciju:

Cipu, Mihai; Dujella, Andrej; Fujita, Yasutsugu
Extensions of a Diophantine triple by adjoining smaller elements II // Periodica mathematica Hungarica (2023) (znanstveni, prihvaćen)
Cipu, M., Dujella, A. & Fujita, Y. (2023) Extensions of a Diophantine triple by adjoining smaller elements II. Prihvaćen za objavljivanje u Periodica mathematica Hungarica. [Preprint].
@unknown{unknown, author = {Cipu, Mihai and Dujella, Andrej and Fujita, Yasutsugu}, year = {2023}, keywords = {Diophantine m-tuples, Pellian equations}, journal = {Periodica mathematica Hungarica}, title = {Extensions of a Diophantine triple by adjoining smaller elements II}, keyword = {Diophantine m-tuples, Pellian equations} }
@unknown{unknown, author = {Cipu, Mihai and Dujella, Andrej and Fujita, Yasutsugu}, year = {2023}, keywords = {Diophantine m-tuples, Pellian equations}, journal = {Periodica mathematica Hungarica}, title = {Extensions of a Diophantine triple by adjoining smaller elements II}, keyword = {Diophantine m-tuples, Pellian equations} }

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





Contrast
Increase Font
Decrease Font
Dyslexic Font