Rad HAZU, Matematičke znanosti, Vol. 30 (2026), 65-73. \( \)

SPLITTING SUMS OF BINARY POLYNOMIALS

Luis H. Gallardo

Univ. Brest, UMR CNRS 6205, Laboratoire de Mathématiques de Bretagne Atlantique, 6, Av. Le Gorgeu, C.S. 93837, Cedex 3, F-29238 Brest, France
e-mail:Luis.Gallardo@univ-brest.fr

Abstract.   We study an analogue of a classical arithmetic problem over the ring of polynomials. We prove that \(m = 5\) is the minimal number such that the sums of any two distinct polynomials in a set of \(m\) polynomials over \(\mathbb{F}_2[x]\) cannot all be of the form \(x^k(x+1)^{\ell}\).

2020 Mathematics Subject Classification.   11T55, 11T06, 05A15, 11B13.

Key words and phrases.   Sums of polynomials, linear factors, characteristic \(2\).

Full text (PDF) (free access)

https://doi.org/10.21857/y26kecdqk9

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