Original scientific paper
https://doi.org/10.21857/y26kecdqk9
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
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 \(x^k(x+1)^{\ell}\).
Keywords
Sums of polynomials; linear factors; characteristic 2
Hrčak ID:
344362
URI
Publication date:
10.2.2026.
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