zbMATH — the first resource for mathematics

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.

11A15 Power residues, reciprocity
11A41 Primes
Full Text: Link