On the Polynomial Quadruples with the Property D(-1;1) (CROSBI ID 237790)
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Bliznac Trebješanin, Marija ; Filipin, Alan ; Jurasić, Ana
engleski
On the Polynomial Quadruples with the Property D(-1;1)
In this paper we prove, under some assumptions, that every polynomial D(-1)-triple in Z[X] can only be extended to a polynomial D(-1 ; 1)- quadruple in Z[X] by polynomials d(+/-). More precisely, if {; ; a, b, c ; d}; ; is a polynomial D(-1 ; 1)-quadruple, then d = d(+/-) = -(a + b + c) +2(abc +/- rst), where r, s and t are polynomials from Z[X] with positive leading coefficients that satisfy ab - 1 = r(2), ac - 1 = s(2) and bc - 1 = t(2) .
Diophantine m-tuples ; polynomials
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