There are infinitely many (-1,1)-Carmichael numbers
Qi-Yang Zheng
TL;DR
This paper proves the existence of infinitely many (-1,1)-Carmichael numbers, which are special composite numbers with a divisibility property related to their prime factors.
Contribution
The paper establishes the first proof that infinitely many (-1,1)-Carmichael numbers exist, expanding understanding of Carmichael number variants.
Findings
Infinitely many (-1,1)-Carmichael numbers exist.
These numbers are square-free, composite, with specific divisibility properties.
The result generalizes previous knowledge about Carmichael numbers.
Abstract
We prove that there exist infinitely many (-1,1)-Carmichael numbers, that is, square-free, composite integers n such that p+1 divides n-1 for each prime p dividing n.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Theories · Advanced Mathematical Identities