ON ELITE PRIMES OF PERIOD FOUR

Abstract

A prime p is elite if all sufficiently large Fermat numbers Fn = 22n + 1 are quadratic nonresidues modulo p. In contrast, p is anti-elite if all sufficiently large Fn are quadratic residues modulo p. The sequence Fn modulo p is necessarily periodic. We give a sequence of pairwise coprime integers whose prime factors are each elite or anti-elite with period four.