Naslov
An irregular D(4)-quadruple cannot be extended to a quintuple

Autori
Filipin, Alan

Izvornik
Acta Arithmetica (0065-1036) 136 (2009), 2; 167-176

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

Ključne riječi
Diophantine m-tuples

Sažetak
A D(4)-m-tuple is a set of m positive integers with the property that the product of any two of them increased by 4 is a perfect square. Moreover, we call a D(4)-quadruple {; ; ; a ; b ; c ; d}; ; ; such that d > max{; ; ; a ; b ; c}; ; ; ; regular if d = a + b + c + 1/2 (abc + rst) ; where r^2 = ab + 4 ; s^2 = ac + 4 ; t^2 = bc + 4: In this paper we prove that any D(4)-quintuple contains a regular D(4)-quadruple.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA