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An irregular D(4)-quadruple cannot be extended to a quintuple (CROSBI ID 144376)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Filipin, Alan
An irregular D(4)-quadruple cannot be extended to a quintuple // Acta Arithmetica, 136 (2009), 2; 167-176
Podaci o odgovornosti
Filipin, Alan
engleski
An irregular D(4)-quadruple cannot be extended to a quintuple
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.
Diophantine m-tuples
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