Journal of Integer Sequences, Vol. 24 (2021), Article 21.1.7

Hypothetical Elite Primes for Mersenne Numbers and Repunits

Amin Witno
Department of Basic Sciences
Philadelphia University
19392 Jordan


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.

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(Concerned with sequences A004064 A102742 A128852 A275377.)

Received August 4 2020; revised version received January 2 2021. Published in Journal of Integer Sequences, January 3 2021.

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