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On the extensions of the Diophantine triples in Gaussian integers
Monatshefte für Mathematik, 197(4) (2022); 535-563. urn:nbn:hr:237:781222
Adžaga, Nikola; Filipin, Alan; Franušić, Zrinka

Institucijski repozitorij: Repozitorij Građevinskog fakulteta Sveučilišta u Zagrebu

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Adžaga, N., Filipin, A. i Franušić, Z. (2022). On the extensions of the Diophantine triples in Gaussian integers. Monatshefte für Mathematik, 197(4)., 535-563. Preuzeto s https://urn.nsk.hr/urn:nbn:hr:237:781222

Adžaga, Nikola, et al. "On the extensions of the Diophantine triples in Gaussian integers." Monatshefte für Mathematik, vol. 197(4), 2022, str. 535-563. https://urn.nsk.hr/urn:nbn:hr:237:781222

Adžaga, Nikola, Alan Filipin i Zrinka Franušić. "On the extensions of the Diophantine triples in Gaussian integers." Monatshefte für Mathematik 197(4) (2022): 535-563. https://urn.nsk.hr/urn:nbn:hr:237:781222

Adžaga, N., Filipin, A. i Franušić, Z. (2022) 'On the extensions of the Diophantine triples in Gaussian integers', Monatshefte für Mathematik, 197(4), str. 535-563. Preuzeto s: https://urn.nsk.hr/urn:nbn:hr:237:781222 (Datum pristupa: 03.11.2024.)

Adžaga N, Filipin A, Franušić Z. On the extensions of the Diophantine triples in Gaussian integers. Monatshefte für Mathematik [Internet]. 2022. [pristupljeno 03.11.2024.];197(4):535-563. Dostupno na: https://urn.nsk.hr/urn:nbn:hr:237:781222

N. Adžaga, A. Filipin i Z. Franušić, "On the extensions of the Diophantine triples in Gaussian integers", Monatshefte für Mathematik, vol. 197(4), str. 535-563, 2022. [Online]. Dostupno na: https://urn.nsk.hr/urn:nbn:hr:237:781222. [Citirano: 03.11.2024.]

Za citiranje koristite ovu mrežnu adresu: https://urn.nsk.hr/urn:nbn:hr:237:781222
Podaci o radu
Naslov (engleski)On the extensions of the Diophantine triples in Gaussian integers
AutorNikola Adžaga
AutorAlan Filipin
AutorZrinka Franušić
Autorova ustanovaSveučilište u Zagrebu
Građevinski fakultet
Znanstveno / umjetničko
područje, polje i grana		TEHNIČKE ZNANOSTI
Građevinarstvo
Sažetak (engleski)
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. In this paper we study the extensibility of a Diophantine triple {; ; k−1, k+1, 16k3−4k}; ; in Gaussian integers Z[i] to a Diophantine quadruple. Similar one- parameter family, {; ; k − 1, k + 1, 4k}; ; , was studied in [9], where it was shown that the extension to a Diophantine quadruple is unique (with an element 16k3 −4k). The family of the triples of the same form {; ; k−1, k+1, 16k^3 −4k}; ; was studied in rational integers in [6]. It appeared as a special case while solving the extensibility problem of Diophantine pair {; ; k − 1, k + 1}; ; , in which it was not possible to use the same method as in the other cases. As authors (Bugeaud, Dujella and Mignotte) point out, the difficulty appears because the gap between k + 1 and 16k^3 − 4k is not sufficiently large. We find the same difficulty here while trying to use Diophantine approximations. Then we partially solve this problem by using linear forms in logarithms.
Ključne riječi (engleski)
Jezikengleski
Vrsta publikacijeZnanstveni rad - Izvorni znanstveni rad
Status objaveObjavljen
Vrsta recenzijeRecenziran - međunarodna recenzija
Verzija publikacijeObjavljena verzija rada (izdavačev PDF)
Naslov časopisaMonatshefte für Mathematik
Brojčani podacivol. 197(4), str. 535-563
e-ISSN1436-5081
URN:NBNurn:nbn:hr:237:781222
Datum objave publikacije2022
Vrsta resursaTekst
Prava pristupaOtvoreni pristup
Uvjeti korištenjaIkona licence Zaštićeno autorskim pravom.
Datum i vrijeme pohrane2024-09-05 05:10:53