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Mersenne Primes in Real Quadratic Fields
Mersenne Primes Real Quadratic Fields Number Theory
2012/5/24
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 Mersenn...
Non-existence of elliptic curves with everywhere good reduction over some real quadratic fields
Non-existence of elliptic curves quadratic fields Number Theory
2011/9/19
Abstract: We prove the non-existence of elliptic curves having good reduction everywhere over some real quadratic fields.