Remarks on a Problem of Eisenstein

Abstract

The fundamental unit of $\mathbb{Z}[\sqrt{N}]$ for square-free $N=5mod8$ is either $\epsilon$ or ${\epsilon }^3$ where $\epsilon$ denotes the fundamental unit of the maximal order of $\Q(\sqrt{N})$. We give infinitely many examples for each case.

arXiv comment4 pages

Cited by in corpus (2)

• Unit groups of maximal orders in totally definite quaternion algebras over real quadratic fields
• On superspecial abelian surfaces and type numbers of totally definite quaternion algebras