There are infinitely many (-1,1)-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.

arXiv commentv1: This paper give new results about numbers which satisfy some conditions. The method we use is a slight modification of [There are infinitely many Carmichael numbers]. We copy some original description in this paper and we will modify it in subsequent versions. v2: typos corrected