Naslov
Diophantine pairs that induce certain Diophantine triples

Autori
Cipu, Mihai ; Filipin, Alan ; Fujita, Yasutsugu

Izvornik
Journal of number theory (0022-314X) 210 (2020); 433-475

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Diophantine m-tuples ; Pellian equations ; linear forms in logarithms

Sažetak
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 this paper, it is shown that any Diophantine triple, the second largest 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. As a corollary, a similar result is obtained under the hypothesis that the two smallest elements have the form $KA^2$, $4KA^4 \pm 4 A$ for some positive integers $A$ and $K \in \{;1, 2, 3, 4\};$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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