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Peer-reviewedCC BY 4.0Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti

Splitting sums of binary polynomials

  • Luis H Gallardo
Open at sourcePDFDOICite

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 F 2 [x] cannot all be of the form x k (x + 1) ℓ .

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Cite

BibTeXRIS
BibTeX
@article{gallardo2026splitting,
  title = {{Splitting sums of binary polynomials}},
  author = {Luis H Gallardo},
  journal = {Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti},
  year = {2026},
  month = oct,
  doi = {10.21857/y26kecdqk9},
  url = {https://univ-brest.hal.science/hal-05775059v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Splitting sums of binary polynomials
AU  - Luis H Gallardo
PY  - 2026
DA  - 2026/10/02
JO  - Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti
DO  - 10.21857/y26kecdqk9
UR  - https://univ-brest.hal.science/hal-05775059v1
AB  - 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 F 2 [x] cannot all be of the form x k (x + 1) ℓ .
SN  - 1845-4100
SN  - 1845-4100
ER  -