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Scientific paper - Original scientific paper
Triples which are D(n)-sets for several n's
Journal of number theory, 184 (2018); 330-341. https://doi.org/10.1016/j.jnt.2017.08.024
Adžaga, Nikola; Dujella, Andrej; Kreso, Dijana; Tadić, Petra

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Adžaga, N., Dujella, A., Kreso, D. & Tadić, P. (2018). Triples which are D(n)-sets for several n's. Journal of number theory, 184., 330-341. doi: 10.1016/j.jnt.2017.08.024

Adžaga, Nikola, et al. "Triples which are D(n)-sets for several n's." Journal of number theory, vol. 184, 2018, pp. 330-341. https://doi.org/10.1016/j.jnt.2017.08.024

Adžaga, Nikola, Andrej Dujella, Dijana Kreso and Petra Tadić. "Triples which are D(n)-sets for several n's." Journal of number theory 184 (2018): 330-341. https://doi.org/10.1016/j.jnt.2017.08.024

Adžaga, N., et al. (2018) 'Triples which are D(n)-sets for several n's', Journal of number theory, 184, pp. 330-341. doi: 10.1016/j.jnt.2017.08.024

Adžaga N, Dujella A, Kreso D, Tadić P. Triples which are D(n)-sets for several n's. Journal of number theory [Internet]. 2018 [cited 2025 April 11];184:330-341. doi: 10.1016/j.jnt.2017.08.024

N. Adžaga, A. Dujella, D. Kreso and P. Tadić, "Triples which are D(n)-sets for several n's", Journal of number theory, vol. 184, pp. 330-341, 2018. [Online]. Available at: https://urn.nsk.hr/urn:nbn:hr:237:688589. [Accessed: 11 April 2025]

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Metadata
Title (english)Triples which are D(n)-sets for several n's
AuthorNikola Adžaga
AuthorAndrej Dujella
AuthorDijana Kreso
AuthorPetra Tadić
Author's institutionUniversity of Zagreb
Faculty of Civil Engineering
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Civil Engineering
Abstract (english)
For a nonzero integer n, a set of distinct nonzero integers {; ; ; ; ; ; ; ; a1, a2, ... , am}; ; ; ; ; ; ; ; such that aiaj + n is a perfect square for all 1 <= i < j <= m, is called a Diophantine m- tuple with the property D(n) or simply D(n)- set. D(1)-sets are known as simply Diophantine m- tuples. Such sets were first studied by Diophantus of Alexandria, and since then by many authors. It is natural to ask if there exists a Diophantine m- tuple (i.e. D(1)-set) which is also a... More D(n)-set for some n not equal to 1. This question was raised by Kihel and Kihel in 2001. They conjectured that there are no Diophantine triples which are also D(n)-sets for some n <> 1. However, the conjecture does not hold, since, for example, {; ; ; ; ; ; ; ; 8, 21, 55}; ; ; ; ; ; ; ; is a D(1) and D(4321)- triple, while {; ; ; ; ; ; ; ; 1, 8, 120}; ; ; ; ; ; ; ; is a D(1) and D(721)- triple. We present several infinite families of Diophantine triples {; ; ; ; ; ; ; ; a, b, c}; ; ; ; ; ; ; ; which are also D(n)- sets for two distinct n's with n <> 1, as well as some Diophantine triples which are also D(n)-sets for three distinct n's with n 6= 1. We further consider some related question Less
Keywords (english)
Languageenglish
Publication typeScientific paper - Original scientific paper
Publication statusPublished
Peer reviewPeer review - international
Publication versionPublished version
Journal titleJournal of number theory
Numberingvol. 184, pp. 330-341
e-ISSN1096-1658
DOIhttps://doi.org/10.1016/j.jnt.2017.08.024
URN:NBNurn:nbn:hr:237:688589
Publication2018
Type of resourceText
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-09-05 10:27:51
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