Publication date: 30 December 2022
Volume: Vol 57
Issue: Svezak 2
Pages: 203-219
DOI: https://doi.org/10.3336/gm.57.2.03
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
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 \(\mathbb{Z}[X]\).
Diophantine \(m\)-tuples, polynomials
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30.12.2022.
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