Large Zsigmondy Primes
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866910520440782848 |
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| author | Avcı, Ömer |
| author_facet | Avcı, Ömer |
| contents | If $a>b$ and $n>1$ are positive integers and $a$ and $b$ are relatively prime integers, then a large Zsigmondy prime for $(a,b,n)$ is a prime $p$ such that $p \,|\, a^n-b^n$ but $p \,\nmid \, a^m-b^m$ for $1 \leq m < n$ and either $p^2 \, | \, a^n - b^n$ or $ p > n + 1$. We classify all the triples of integers $(a, b, n)$ for which no large Zsigmondy prime exists. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_06136 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Large Zsigmondy Primes Avcı, Ömer Number Theory 11A41 G.0 If $a>b$ and $n>1$ are positive integers and $a$ and $b$ are relatively prime integers, then a large Zsigmondy prime for $(a,b,n)$ is a prime $p$ such that $p \,|\, a^n-b^n$ but $p \,\nmid \, a^m-b^m$ for $1 \leq m < n$ and either $p^2 \, | \, a^n - b^n$ or $ p > n + 1$. We classify all the triples of integers $(a, b, n)$ for which no large Zsigmondy prime exists. |
| title | Large Zsigmondy Primes |
| topic | Number Theory 11A41 G.0 |
| url | https://arxiv.org/abs/2011.06136 |