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December 2018 On the Polynomial Quadruples with the Property $D(-1;1)$
Marija BLIZNAC TREBJEŠANIN, Alan FILIPIN, Ana JURASIĆ
Tokyo J. Math. 41(2): 527-540 (December 2018). DOI: 10.3836/tjm/1502179250

Abstract

In this paper we prove, under some assumptions, that every polynomial $D(-1)$-triple in $\mathbb{Z}[X]$ can only be extended to a polynomial $D(-1;1)$-quadruple in $\mathbb{Z}[X]$ by polynomials $d^{\pm}$. More precisely, if $\{a,b,c;d\}$ is a polynomial $D(-1;1)$-quadruple, then $$d=d^{\pm}=-(a+b+c)+2(abc\pm rst)\,,$$ where $r$, $s$ and $t$ are polynomials from $\mathbb{Z}[X]$ with positive leading coefficients that satisfy $ab-1=r^2$, $ac-1=s^2$ and $bc-1=t^2$.

Citation

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Marija BLIZNAC TREBJEŠANIN. Alan FILIPIN. Ana JURASIĆ. "On the Polynomial Quadruples with the Property $D(-1;1)$." Tokyo J. Math. 41 (2) 527 - 540, December 2018. https://doi.org/10.3836/tjm/1502179250

Information

Published: December 2018
First available in Project Euclid: 20 November 2017

zbMATH: 07053490
MathSciNet: MR3908808
Digital Object Identifier: 10.3836/tjm/1502179250

Subjects:
Primary: 11D09
Secondary: 11D45

Rights: Copyright © 2018 Publication Committee for the Tokyo Journal of Mathematics

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Vol.41 • No. 2 • December 2018
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