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A note on the generalization of elite primes. (English) Zbl 1228.11007
An elite prime is an odd prime $$p$$ such that the Fermat number $$F_n=2^{2^n}+1$$ is a quadratic nonresidue modulo $$p$$ for all large enough $$n$$. This notion has been extended in previous works to elite primes with respect to generalized Fermat numbers $$F_{b,n}=b^{2^n}+1$$ for some fixed positive integer $$b$$. In the paper under review, the authors propose another extension of this notion involving the numbers $$F_{b,n}/2$$ being quadratic nonresidues modulo $$p$$, where $$b\geq 3$$ is a fixed odd integer. They prove a number of results concerning the elite primes in this set–up and present some numerical results.

##### MSC:
 11A15 Power residues, reciprocity 11A41 Primes
##### Keywords:
elite primes; generalized Fermat numbers
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