Question
Find the inverse of $1+\sqrt{2}$ in $Z[\sqrt{2}]$. What is the multiplicative order of $1+\sqrt{2}$ ?
Step 1
Step 1: To find the inverse of \(1+\sqrt{2}\) in \( \mathbb{Z}[\sqrt{2}] \), we need to find an element \(x + y\sqrt{2}\) such that \((1+\sqrt{2})(x+y\sqrt{2}) = 1\) for some integers \(x\) and \(y\). Show more…
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