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
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.
Full version: pdf,
(Concerned with sequence
Received May 2 2012;
revised version received May 21 2012.
Published in Journal of Integer Sequences, June 11 2012.
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