Word Count : 181

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Let ( R = \mathbb{Z}[\sqrt{-7}] = {a + b\sqrt{-7} \mid a, b \in \mathbb{Z}} ). An element ( u = a + b\sqrt{-7} ) is a unit if there exists ( v = c + d\sqrt{-7} \in R ) such that ( uv = 1 ______ _______ ___ ___ ____.
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