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Scientific paper - Original scientific paper
Diophantine pairs that induce certain Diophantine triples
Journal of number theory, 210 (2020); 433-475. urn:nbn:hr:237:853491
Cipu, Mihai; Filipin, Alan; Fujita, Yasutsugu

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Cipu, M., Filipin, A. & Fujita, Y. (2020). Diophantine pairs that induce certain Diophantine triples. Journal of number theory, 210., 433-475. Retrieved from https://urn.nsk.hr/urn:nbn:hr:237:853491

Cipu, Mihai, et al. "Diophantine pairs that induce certain Diophantine triples." Journal of number theory, vol. 210, 2020, pp. 433-475. https://urn.nsk.hr/urn:nbn:hr:237:853491

Cipu, Mihai, Alan Filipin and Yasutsugu Fujita. "Diophantine pairs that induce certain Diophantine triples." Journal of number theory 210 (2020): 433-475. https://urn.nsk.hr/urn:nbn:hr:237:853491

Cipu, M., Filipin, A. and Fujita, Y. (2020) 'Diophantine pairs that induce certain Diophantine triples', Journal of number theory, 210, pp. 433-475. Available at: https://urn.nsk.hr/urn:nbn:hr:237:853491 (Accessed 02 October 2024)

Cipu M, Filipin A, Fujita Y. Diophantine pairs that induce certain Diophantine triples. Journal of number theory [Internet]. 2020 [cited 2024 October 02];210:433-475. Available at: https://urn.nsk.hr/urn:nbn:hr:237:853491

M. Cipu, A. Filipin and Y. Fujita, "Diophantine pairs that induce certain Diophantine triples", Journal of number theory, vol. 210, pp. 433-475, 2020. [Online]. Available at: https://urn.nsk.hr/urn:nbn:hr:237:853491. [Accessed: 02 October 2024]

Metadata
Title (english)Diophantine pairs that induce certain Diophantine triples
AuthorMihai Cipu
AuthorAlan Filipin
AuthorYasutsugu Fujita
Author's institutionUniversity of Zagreb
Faculty of Civil Engineering
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract (english)
Diophantine tuples are sets of positive integers with the property that the product of any two elements in the set increased by the unity is a square. In the main theorem of this paper it is shown that any Diophantine triple, the second largest element of which is between the square and four times the square of the smallest one, is uniquely extended to a Diophantine quadruple by joining an element exceeding the largest element in the triple. A similar result is obtained under the hypothesis that the two smallest elements have the form T2+2T, 4T4+8T3−4Tfor some positive integer T, which we encounter as an exceptional case. The main theorem implies that the same is valid for triples with smallest elements KA2, 4KA4±4Afor some positive integers Aand K∈{1, 2, 3, 4}.
Keywords (english)
Languageenglish
Publication typeScientific paper - Original scientific paper
Publication statusPublished
Peer reviewPeer review - international
Publication versionPublished version
Journal titleJournal of number theory
Numberingvol. 210, pp. 433-475
e-ISSN1096-1658
URN:NBNurn:nbn:hr:237:853491
Publication2020
Type of resourceText
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-09-05 06:16:37