Primes modulo which almost all Fermat numbers are primitive roots


A prime p is called elite, or anti-elite, when all but finitely many      Fermat numbers are quadratic nonresidues or residues, respectively, modulo p. It is known that if the multiplicative order of 2 modulo p is of the form 2^s\times 5, where s\geq 2, then the prime p is either elite or anti-elite. Modulo elite primes of this kind, we describe some criteria by which all sufficiently large Fermat numbers be primitive roots, or all nonprimitive roots.

DOI Code: 10.1285/i15900932v30n1p133

elite primes; Fermat numbers

Classification: 11A07, 11A41

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