Journal of Integer Sequences, Vol. 11 (2008), Article 08.3.1

On Generalized Elite Primes

Tom Müller and Andreas Reinhart
Institut für Cusanus-Forschung an der
Universität und der Theologischen Fakultät Trier
Domfreihof 3
D-54290 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 derived.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequence A102742 .)

Received May 8 2008; revised version received July 8 2008. Published in Journal of Integer Sequences, July 25 2008.

Return to Journal of Integer Sequences home page