Hypothetical Elite Primes for Mersenne Numbers and Repunits
Department of Basic Sciences
We study prime numbers p that have the property that the numbers
(bq-1)/(b-1) are quadratic residues
modulo p for all sufficiently large primes q. We give
a practical criterion for testing for such primes with respect to
the base b and, for certain values of b, we find a
connection between these primes and anti-elite primes, i.e., where
b2n+1 are quadratic residues modulo
p for all large n.
Full version: pdf,
(Concerned with sequences
Received August 4 2020; revised version received January 2 2021.
Published in Journal of Integer Sequences,
January 3 2021.
Journal of Integer Sequences home page