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Pregled bibliografske jedinice broj: 867446

On the extension of D(-8k^2)-pair (8k^2, 8k^2+1)


Adžaga, Nikola; Filipin, Alan
On the extension of D(-8k^2)-pair (8k^2, 8k^2+1) // Moscow Mathematical Journal, 17 (2017), 2; 165-174 (međunarodna recenzija, članak, znanstveni)


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Naslov
On the extension of D(-8k^2)-pair (8k^2, 8k^2+1)

Autori
Adžaga, Nikola ; Filipin, Alan

Izvornik
Moscow Mathematical Journal (1609-3321) 17 (2017), 2; 165-174

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Diophantine m-tuples, Pell equations, elementary proofs

Sažetak
Let k be a positive integer. Triple {; ; 1, 8k^2, 8k^2+1}; ; has the property that the product of any two of its distinct elements subtracted by 8k^2 is a perfect square. By elementary means, we show that this triple can be extended to at most a quadruple retaining this property, i.e. if {; ; 1, 8k^2, 8k^2+1, d}; ; has the same property, then d is uniquely determined (d=32k^2+1). Moreover, we show that even the pair {; ; 8k^2, 8k^2+1}; ; can be extended in the same manner to at most a quadruple (the third and fourth element can only be 1 and 32k^2+1). At the end, we suggest considering a similar problem of extending the triple {; ; 1, 2k^2, 2k^2+2k+1}; ; with a similar property as possible future research direction.

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) ( POIROT)

Ustanove:
Građevinski fakultet, Zagreb

Profili:

Avatar Url Alan Filipin (autor)

Avatar Url Nikola Adžaga (autor)

Citiraj ovu publikaciju

Adžaga, Nikola; Filipin, Alan
On the extension of D(-8k^2)-pair (8k^2, 8k^2+1) // Moscow Mathematical Journal, 17 (2017), 2; 165-174 (međunarodna recenzija, članak, znanstveni)
Adžaga, N. & Filipin, A. (2017) On the extension of D(-8k^2)-pair (8k^2, 8k^2+1). Moscow Mathematical Journal, 17 (2), 165-174.
@article{article, year = {2017}, pages = {165-174}, keywords = {Diophantine m-tuples, Pell equations, elementary proofs}, journal = {Moscow Mathematical Journal}, volume = {17}, number = {2}, issn = {1609-3321}, title = {On the extension of D(-8k\^{}2)-pair (8k\^{}2, 8k\^{}2+1)}, keyword = {Diophantine m-tuples, Pell equations, elementary proofs} }
@article{article, year = {2017}, pages = {165-174}, keywords = {Diophantine m-tuples, Pell equations, elementary proofs}, journal = {Moscow Mathematical Journal}, volume = {17}, number = {2}, issn = {1609-3321}, title = {On the extension of D(-8k\^{}2)-pair (8k\^{}2, 8k\^{}2+1)}, keyword = {Diophantine m-tuples, Pell equations, elementary proofs} }

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





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