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Scientific paper - Original scientific paper
The extension of the D(-k)-pair {k, k+1) to a quadruple
Periodica mathematica Hungarica, 85(1) (2022); 148-163. urn:nbn:hr:237:432136
Adžaga, Nikola; Filipin, Alan; Fujita, Yasutsugu

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Adžaga, N., Filipin, A. & Fujita, Y. (2022). The extension of the D(-k)-pair {k, k+1) to a quadruple. Periodica mathematica Hungarica, 85(1)., 148-163. Retrieved from https://urn.nsk.hr/urn:nbn:hr:237:432136

Adžaga, Nikola, et al. "The extension of the D(-k)-pair {k, k+1) to a quadruple." Periodica mathematica Hungarica, vol. 85(1), 2022, pp. 148-163. https://urn.nsk.hr/urn:nbn:hr:237:432136

Adžaga, Nikola, Alan Filipin and Yasutsugu Fujita. "The extension of the D(-k)-pair {k, k+1) to a quadruple." Periodica mathematica Hungarica 85(1) (2022): 148-163. https://urn.nsk.hr/urn:nbn:hr:237:432136

Adžaga, N., Filipin, A. and Fujita, Y. (2022) 'The extension of the D(-k)-pair {k, k+1) to a quadruple', Periodica mathematica Hungarica, 85(1), pp. 148-163. Available at: https://urn.nsk.hr/urn:nbn:hr:237:432136 (Accessed 02 October 2024)

Adžaga N, Filipin A, Fujita Y. The extension of the D(-k)-pair {k, k+1) to a quadruple. Periodica mathematica Hungarica [Internet]. 2022 [cited 2024 October 02];85(1):148-163. Available at: https://urn.nsk.hr/urn:nbn:hr:237:432136

N. Adžaga, A. Filipin and Y. Fujita, "The extension of the D(-k)-pair {k, k+1) to a quadruple", Periodica mathematica Hungarica, vol. 85(1), pp. 148-163, 2022. [Online]. Available at: https://urn.nsk.hr/urn:nbn:hr:237:432136. [Accessed: 02 October 2024]

Metadata
Title (english)The extension of the D(-k)-pair {k, k+1) to a quadruple
AuthorNikola Adžaga
AuthorAlan Filipin
AuthorYasutsugu Fujita
Author's institutionUniversity of Zagreb
Faculty of Civil Engineering
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Civil Engineering
Abstract (english)
Let n be a non-zero integer. A set of m positive integers {; ; ; a_1, a_2, ... , a_m}; ; ; is called a D(n)- m-tuple if a_ia_j + n is a perfect square for all 1 <= i < j <= m. Let k be a positive integer. In this paper, we prove that if {; ; ; k, k+1, c, d}; ; ; is a D(-k)-quadruple with c>1, then d=1. The proof relies not only on standard methods in this field (Baker's linear forms in logarithms and hypergeometric method), but also on some less typical elementary arguments dealing with recurrences, as well as a relatively new method for determination of integral points on hyperelliptic curves.
Keywords (english)
Languageenglish
Publication typeScientific paper - Original scientific paper
Publication statusPublished
Peer reviewPeer review - international
Publication versionPublished version
Journal titlePeriodica mathematica Hungarica
Numberingvol. 85(1), pp. 148-163
e-ISSN1588-2829
URN:NBNurn:nbn:hr:237:432136
Publication2022
Type of resourceText
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-09-05 05:15:24