Original scientific paper

https://doi.org/10.3336/gm.57.2.03

On the existence of $D(-3)$-quadruples over $\mathbb{Z}$

Alan Filipin ; Faculty of Civil Engineering, University of Zagreb, 10 000 Zagreb, Croatia
Ana Jurasić ; Faculty of Mathematics, University of Rijeka, 51 000 Rijeka, Croatia

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Abstract

In this paper we prove that there does not exist a set of four non-zero polynomials from $\mathbb{Z}[X]$, not all constant, such that the product of any two of its distinct elements decreased by $3$ is a square of a polynomial from $\mathbb{Z}[X]$.

Keywords

Diophantine $m$-tuples, polynomials

Hrčak ID:

289612

URI

https://hrcak.srce.hr/289612

Publication date:

30.12.2022.

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