1. CMB Online first
|Variants of Korselt's Criterion|
Under sufficiently strong assumptions about the first term in an arithmetic progression, we prove that for any integer $a$, there are infinitely many $n\in \mathbb N$ 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 $p|n$.
Keywords:Carmichael number, pseudoprime, Korselt's Criterion, primes in arithmetic progressions
2. CMB 2007 (vol 50 pp. 158)