Naslov
Doubly regular Diophantine quadruples

Autori
Dujella, Andrej ; Petričević, Vinko

Izvornik
Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-Matematicas (1578-7303) 114 (2020); 189, 8

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

Ključne riječi
Diophantine quadruples ; regular quadruples ; elliptic curves

Sažetak
For a nonzero integer n, a set of m distinct nonzero integers {; ; ; ; ; ; ; a1, a2, . . . , am}; ; ; ; ; ; ; such that aiaj + n is a perfect square for all 1 ≤ i < j ≤ m, is called a D(n)-m-tuple. In this paper, by using properties of so-called regular Diophantine m- tuples and certain family of elliptic curves, we show that there are infinitely many essentially different sets consisting of perfect squares which are simultaneously D(n1)- quadruples and D(n2)-quadruples with distinct non- zero squares n1 and n2.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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