Variants of Korselt’s Criterion

Abstract

AbstractUnder sufficiently strong assumptions about the first term in an arithmetic progression, we prove that for any integer a, there are infinitely many n ∊ ℕ such that for each prime factor p | n, we have p−a | n−a. This can be seen as a generalization of Carmichael numbers, which are integers n such that p − 1 | n − 1 for every p | n.