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Any D(4)-quintuple contains a regular quadruple (CROSBI ID 541343)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija

Filipin, Alan Any D(4)-quintuple contains a regular quadruple // Canadian Number Theory Association X Meeting. Waterloo: University of Waterloo, 2008

Podaci o odgovornosti

Filipin, Alan

engleski

Any D(4)-quintuple contains a regular quadruple

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.

D(4)-m-tuple

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

Podaci o prilogu

2008.

objavljeno

Podaci o matičnoj publikaciji

Canadian Number Theory Association X Meeting

Waterloo: University of Waterloo

Podaci o skupu

Canadian Number Theory Association X Meeting (CNTA X)

predavanje

13.07.2008-18.07.2008

Waterloo, Kanada

Povezanost rada

Matematika