Naslov
Any D(4)-quintuple contains a regular quadruple

Autori
Filipin, Alan

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Canadian Number Theory Association X Meeting / - Waterloo : University of Waterloo, 2008

Skup
Canadian Number Theory Association X Meeting (CNTA X)

Mjesto i datum
Waterloo, Kanada, 13.07.2008. - 18.07.2008

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
D(4)-m-tuple

Sažetak
A set of m positive integers is called a D(4)-m-tuple, if the product of any two of its distinct elements 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, s and t are positive integers given by ab+4=r^2, ac+4=s^2, bc+4=t^2. There is a conjecture that all D(4)-quadruples are regular, which would imply that there does not exist a D(4)-quintuple. It is proven that there is no D(4)-sextuple. In this talk we prove that any D(4)-quintuple contains a regular quadruple, i.e. that we cannot extend an irregular D(4)-quadruple with a larger element.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA