Journal of Integer Sequences, Vol. 15 (2012), Article 12.5.6

Mersenne Primes in Real Quadratic Fields

Sushma Palimar and B. R. Shankar
Department of Mathematical and Computational Sciences
National Institute of Technology Karnataka, Surathkal


The concept of Mersenne primes is studied in real quadratic fields with class number one. Computational results are given. The field Q(√ 2) is studied in detail with a focus on representing Mersenne primes in the form x2 + 7y2. It is also proved that x is divisible by 8 and y ≡ ± 3 (mod 8), generalizing a result of F. Lemmermeyer, first proved by H. W. Lenstra and P. Stevenhagen using Artin's reciprocity law.

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(Concerned with sequence A033207.)

Received May 2 2012; revised version received May 21 2012. Published in Journal of Integer Sequences, June 11 2012.

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