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arXiv · 2011.06136

Large Zsigmondy Primes

Ömer Avcı
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Abstract

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.

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Ömer Avcı. 2020-11-12. Large Zsigmondy Primes. https://doi.org/10.5281/zenodo.12685673

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