Some pseudoprimes and related numbers having special forms

Abstract

We give an example of a pseudoprime which is itself of the form 2 n − 2 {2^n} - 2 , answering a question posed by A. Rotkiewicz, show that Lehmer’s example of an even pseudoprime having three prime factors is not unique, and answer a question of Benkoski concerning the solutions of 2 n − 2 ≡ 1 ( mod n ) {2^{n - 2}} \equiv 1\;\pmod n .