Splitting sums of binary polynomials
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914328467210240 |
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| author | Gallardo, Luis H. |
| author_facet | Gallardo, Luis H. |
| contents | 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 $x^k(x+1)^{\ell}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13111 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Splitting sums of binary polynomials Gallardo, Luis H. Number Theory 11T55, 11T06, 05A15, 11B13 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 $x^k(x+1)^{\ell}$. |
| title | Splitting sums of binary polynomials |
| topic | Number Theory 11T55, 11T06, 05A15, 11B13 |
| url | https://arxiv.org/abs/2602.13111 |