Any D(4)-quintuple contains a regular quadruple (CROSBI ID 541343)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
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
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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