Naslov
Generalization of a problem of Diophantus

Autori
Dujella, Andrej

Izvornik
Acta Arithmetica (0065-1036) 65 (1993), 1; 15-27

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

Ključne riječi
Diophantine quadruples

Sažetak
In this paper we consider some problems of existence of sets of four natural numbers with property D(n), for any integer n. We prove that, for all e in Z, there exist infinite numbers of sets of four natural numbers with property D(e^2). Indeed, we show how a set {; ; a, b}; ; with property D(e^2) can be extended to a set {; ; a, b, c, d}; ; with the same property, if ab is not a perfect square. The general case is also considered: sets with property D(n), when n need not be a perfect square. The main results is: If n is an integer which is not of the form 4k + 2 and n is not an elements of S = {; ; 3, 5, 8, 12, 20, − 1, − 3, − 4}; ; then there exists at least one set of four natural numbers with property D(n).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA