Simple Remarks on Carmichael Numbers

Abstract

An odd composite number n for which a^n-1 ≡ 1 (mod n) for all integers a coprime to n is called a Carmichael number. This paper shows that some class of Carmichael numbers which have relatively large prime factors can be recognized in deterministic polynomial time under the assumption of the Extended Riemann Hypothesis (ERH). Also some related problems are discussed.