Word Count : 207

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Let ( \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 it has a multiplicative inverse in ( \mathbb{Z}[\sqrt{-7}] ), i.e., there exists ( __________ _____ ______ __________ ______ __________ _________ ____ ____ ______ _________.
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