On the irreducibility of the non-cyclotomic part of most 0,1-polynomials with few terms
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912540852748288 |
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| author | Filaseta, Michael Kalogirou, Alexandros |
| author_facet | Filaseta, Michael Kalogirou, Alexandros |
| contents | We provide an alternative exposition of a result due to Schinzel. Fix an integer $k \ge 2$. For almost all choices of positive integers $n_{1} < \cdots < n_{k}$, we show that the polynomial $F(x) = 1 + x^{n_{1}} + \cdots + x^{n_{k}}$, removed of its cyclotomic factors, is irreducible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the irreducibility of the non-cyclotomic part of most 0,1-polynomials with few terms Filaseta, Michael Kalogirou, Alexandros Number Theory 11R09 (Primary) 11C08, 12E05 (Secondary) We provide an alternative exposition of a result due to Schinzel. Fix an integer $k \ge 2$. For almost all choices of positive integers $n_{1} < \cdots < n_{k}$, we show that the polynomial $F(x) = 1 + x^{n_{1}} + \cdots + x^{n_{k}}$, removed of its cyclotomic factors, is irreducible. |
| title | On the irreducibility of the non-cyclotomic part of most 0,1-polynomials with few terms |
| topic | Number Theory 11R09 (Primary) 11C08, 12E05 (Secondary) |
| url | https://arxiv.org/abs/2508.12242 |