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Remarks on a Problem of Eisenstein

Roger C. Alperin
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Abstract

The fundamental unit of $\Z[\sqrt{N}]$ for square-free $N=5 mod 8$ is either $ε$ or $ε^3$ where $ε$ denotes the fundamental unit of the maximal order of $\Q(\sqrt{N})$. We give infinitely many examples for each case.

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Roger C. Alperin. 2006-08-30. Remarks on a Problem of Eisenstein. https://arxiv.org/abs/math/0608741

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