Glasnik Matematicki, Vol. 57, No. 2 (2022), 203-219. \( \)

ON THE EXISTENCE OF \(D(-3)\)-QUADRUPLES OVER \(\mathbb{Z}\)

Alan Filipin and Ana Jurasić

Faculty of Civil Engineering, University of Zagreb, 10 000 Zagreb, Croatia
e-mail:filipin@grad.hr

Faculty of Mathematics, University of Rijeka, 51 000 Rijeka, Croatia
e-mail:ajurasic@math.uniri.hr

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 \(\mathbb{Z}[X]\).

2020 Mathematics Subject Classification.   11D09, 11D45

Key words and phrases.   Diophantine \(m\)-tuples, polynomials

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

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