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arXiv · 1508.05547

Infinitude of $k$-Lehmer numbers which are not Carmichael

Nathan McNew·Thomas Wright
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Abstract

In this paper, we prove that there are infinitely many $n$ for which $rad(φ(n))|n-1$ but $n$ is not a Carmichael number. Additionally, we prove that for any $k\geq 3$, there exist infinitely many $n$ such that $φ(n)|(n-1)^k$ but $φ(n)\nmid (n-1)^{k-1}$. The constructs that we consider here are generalizations of Carmichael and Lehmer numbers, respectively, that were first formulated by Grau and Oller-Marcén.

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Nathan McNew, Thomas Wright. 2015-08-22. Infinitude of $k$-Lehmer numbers which are not Carmichael. https://arxiv.org/abs/1508.05547

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