Word Count : 258

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The units in a number ring like \(\mathbb{Z}[\sqrt{-71}]\) are the elements that have a multiplicative inverse within the ring. To find the units in \(\mathbb{Z}[\sqrt{-71}]\), we need to look for numbers \( \alpha = a + b\sqrt{-71} \), where \( a, b \in \mathbb{Z} \), such that \( \alpha \) has _____ ________ _____ ___ ______ __________ _________ ___ ______ ____.
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