Geodesic
A necessary and sufficient condition for the primality of Fermat numbers
Mathematica Bohemica, Tome 126 (2001) no. 3, pp. 541-549

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MR Zbl
We examine primitive roots modulo the Fermat number $F_m=2^{2^m}+1$. We show that an odd integer $n\ge 3$ is a Fermat prime if and only if the set of primitive roots modulo $n$ is equal to the set of quadratic non-residues modulo $n$. This result is extended to primitive roots modulo twice a Fermat number.
We examine primitive roots modulo the Fermat number $F_m=2^{2^m}+1$. We show that an odd integer $n\ge 3$ is a Fermat prime if and only if the set of primitive roots modulo $n$ is equal to the set of quadratic non-residues modulo $n$. This result is extended to primitive roots modulo twice a Fermat number.
DOI : 10.21136/MB.2001.134197
Classification : 11A07, 11A15, 11A41, 11A51
Keywords: Fermat numbers; primitive roots; primality; Sophie Germain primes 
Křížek, Michal; Somer, Lawrence. A necessary and sufficient condition for the primality of Fermat numbers. Mathematica Bohemica, Tome 126 (2001) no. 3, pp. 541-549. doi: 10.21136/MB.2001.134197
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