The degrees of irreducible factors of binomials and multiplicativity of the n-Hartley condition
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914298107789312 |
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| author | Bolan, Matthew Williams, Ben |
| author_facet | Bolan, Matthew Williams, Ben |
| contents | We prove that, over a field of characteristic $0$, the degrees of factors of a binomial $t^n-α$ are divisible by the least such degree. As a consequence, we deduce that for relatively prime natural numbers $m,n$, a polynomial has the $mn$-Hartley condition if and only if it has the $m$-Hartley and $n$-Hartley conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00578 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The degrees of irreducible factors of binomials and multiplicativity of the n-Hartley condition Bolan, Matthew Williams, Ben Number Theory 12D05 (Primary) 57K14 (Secondary) We prove that, over a field of characteristic $0$, the degrees of factors of a binomial $t^n-α$ are divisible by the least such degree. As a consequence, we deduce that for relatively prime natural numbers $m,n$, a polynomial has the $mn$-Hartley condition if and only if it has the $m$-Hartley and $n$-Hartley conditions. |
| title | The degrees of irreducible factors of binomials and multiplicativity of the n-Hartley condition |
| topic | Number Theory 12D05 (Primary) 57K14 (Secondary) |
| url | https://arxiv.org/abs/2602.00578 |