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A necessary and sufficient condition for the primality of Fermat numbers
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 …