On the finiteness of Carmichael numbers with Fermat factors and $L=2^{\alpha}P^2$

Yu Tsumura

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arXiv · 1710.01321

On the finiteness of Carmichael numbers with Fermat factors and $L=2^{\alpha}P^2$

Yu Tsumura

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Abstract

Let $m$ be a Carmichael number and let $L$ be the least common multiple of $p-1$, where $p$ runs over the prime factors of $m$. We determine all the Carmichael numbers $m$ with a Fermat prime factor such that $L=2^{\alpha}P^2$, where $k\in \mathbb{N}$ and $P$ is an odd prime number. There are eleven such Carmichael numbers.

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Yu Tsumura. 2017-10-03. On the finiteness of Carmichael numbers with Fermat factors and $L=2^{\alpha}P^2$. https://arxiv.org/abs/1710.01321

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