Diophantine pairs that induce certain Diophantine triples

Znanstveni rad - Izvorni znanstveni rad

• Autor: Mihai Cipu
• Autor: Alan Filipin
• Autor: Yasutsugu Fujita
• Autorova ustanova: Sveučilište 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): Diophantine m-tuples, Pellian equations, Linear forms in logarithms
• Jezik: engleski
• Vrsta publikacije: Znanstveni rad - Izvorni znanstveni rad
• Status objave: Objavljen
• Vrsta recenzije: Recenziran - međunarodna recenzija
• Verzija publikacije: Objavljena verzija rada (izdavačev PDF)
• Naslov časopisa: Journal of number theory
• Brojčani podaci: vol. 210, str. 433-475
• e-ISSN: 1096-1658
• URN:NBN: urn:nbn:hr:237:853491
• Datum objave publikacije: 2020
• Vrsta resursa: Tekst
• Prava pristupa: Otvoreni pristup
• Datum i vrijeme pohrane: 2024-09-05 06:16:37