Sushma Palimar, Shankar B. R
Published 2012-05-02Version 1
The concept of Mersenne primes is studied in real quadratic fields of class number 1. Computational results are given. The field $Q(\sqrt{2})$ is studied in detail with a focus on representing Mersenne primes in the form $x^{2}+7y^{2}$. It is also proved that $x$ is divisible by 8 and $y\equiv \pm3\pmod{8}$ generalizing the result of F Lemmermeyer, first proved in \cite{LS} using Artin's Reciprocity law.
A short note on the divisibility of class numbers of real quadratic fields
Class number one problem for the real quadratic fields $\mathbb{Q}({\sqrt{m^2+2r}})$
The distribution of class numbers in a special family of real quadratic fields
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