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 _________ _____ __________ _________ __________ ________ ______ ____.
__________ _____ ______ ___ _____ ____ ____ _________ _____ _______.
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______ ________ ________ _______ ___ __________ _____ ____ __________ ________ ____.
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__________ ____ ___ _____ _______ _________ _____.
________ ________ _________ ____ ____ _______ ___ ____ _____ _____ ______.
____ _____ _________ ________ _____ _________ _________ ________ ____.
______ _____ __________ ______ ______ _________.
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_______ ____ _________ ________ _________ _________.
_______ _____ ________ ______ _________ ______ _____ ___.
_______ _______ _________ ______ ________ _________ _______ __________ _____.
_________ __________ __________ ____ _____.
________ _______ ______ _______ _______ __________ ______ _________.
_______ _______ _______ _________ ______ ______ ______ ________ _______ ___ _______.
_____ _______ __________ ____ _________ ________ ________ ____ _______ ____ ________ _________.
_________.
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