Geodesic
On generalized elite primes
Journal of integer sequences, Tome 11 (2008) no. 3
A prime number $p$ is called $b$-elite if only finitely many generalized Fermat numbers $F_{b,n} = b^{2^{n}}+1$ are quadratic residues to $p$. So far, only the case $b = 2$ was subjected to theoretical and experimental researches by several authors. Most of the results obtained for this special case can be generalized for all bases $b > 2$. Moreover, the generalization allows an insight to more general structures in which standard elite primes are embedded. We present selected computational results from which some conjectures are derived.
Classification : 11A15, 11A41
Keywords: elite primes, generalized Fermat numbers 
@article{JIS_2008__11_3_a0,
     author = {M\"uller,  Tom and Reinhart,  Andreas},
     title = {On generalized elite primes},
     journal = {Journal of integer sequences},
     year = {2008},
     volume = {11},
     number = {3},
     zbl = {1204.11008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2008__11_3_a0/}
}
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Müller,  Tom; Reinhart,  Andreas. On generalized elite primes. Journal of integer sequences, Tome 11 (2008) no. 3. http://geodesic.mathdoc.fr/item/JIS_2008__11_3_a0/