Variants of Korselt's Criterion

摘要

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