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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

Institucijski repozitorij: Repozitorij Građevinskog fakulteta Sveučilišta u Zagrebu

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

Cipu, Mihai, Alan Filipin i 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. i Fujita, Y. (2020) 'Diophantine pairs that induce certain Diophantine triples', Journal of number theory, 210, str. 433-475. Preuzeto s: https://urn.nsk.hr/urn:nbn:hr:237:853491 (Datum pristupa: 27.12.2024.)

Cipu M, Filipin A, Fujita Y. Diophantine pairs that induce certain Diophantine triples. Journal of number theory [Internet]. 2020. [pristupljeno 27.12.2024.];210:433-475. Dostupno na: https://urn.nsk.hr/urn:nbn:hr:237:853491

M. Cipu, A. Filipin i Y. Fujita, "Diophantine pairs that induce certain Diophantine triples", Journal of number theory, vol. 210, str. 433-475, 2020. [Online]. Dostupno na: https://urn.nsk.hr/urn:nbn:hr:237:853491. [Citirano: 27.12.2024.]

Za citiranje koristite ovu mrežnu adresu: https://urn.nsk.hr/urn:nbn:hr:237:853491
Podaci o radu
Naslov (engleski)Diophantine pairs that induce certain Diophantine triples
AutorMihai Cipu
AutorAlan Filipin
AutorYasutsugu Fujita
Autorova ustanovaSveučilište u Zagrebu
Građevinski fakultet
Znanstveno / umjetničko
područje, polje i grana		PRIRODNE ZNANOSTI
Matematika
Sažetak (engleski)
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}.
Ključne riječi (engleski)
Jezikengleski
Vrsta publikacijeZnanstveni rad - Izvorni znanstveni rad
Status objaveObjavljen
Vrsta recenzijeRecenziran - međunarodna recenzija
Verzija publikacijeObjavljena verzija rada (izdavačev PDF)
Naslov časopisaJournal of number theory
Brojčani podacivol. 210, str. 433-475
e-ISSN1096-1658
URN:NBNurn:nbn:hr:237:853491
Datum objave publikacije2020
Vrsta resursaTekst
Prava pristupaOtvoreni pristup
Uvjeti korištenjaIkona licence Zaštićeno autorskim pravom.
Datum i vrijeme pohrane2024-09-05 06:16:37