Sequences in finite fields yielding divisors of Mersenne, Fermat and Lehmer numbers, II

Abstract

Let $\rho$ be an odd prime $\ge 11.$ In Part I, starting from an $M$-cycle in a finite field $\mathbb{F}_\rho$, we have established how the divisors of Mersenne, Fermat and Lehmer numbers arise. The converse question is taken up in this Part with the introduction of an arithmetic function and the notion of a split-associated prime.