On Generalized Elite Primes
Tom Müller and Andreas Reinhart
Institut für Cusanus-Forschung an der
Universität und der Theologischen Fakultät Trier
A prime number p is called b-elite if only finitely many
generalized Fermat numbers
Fb,n = b2n+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
Full version: pdf,
(Concerned with sequence
Received May 8 2008;
revised version received July 8 2008.
Published in Journal of Integer Sequences, July 25 2008.
Journal of Integer Sequences home page