Find all integers $a$ and $b$ such that: $$|a^2 -2b^2|=1$$ The solutions to this equation are related to the units of the ring $\mathbb{Z}[\sqrt{2}]$.
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You are right. Note that $a+b\sqrt{2}$ is a unit if and only if $a^2-2b^2=\pm1$. – Dietrich Burde Aug 02 '18 at 11:46
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This equation can be solved using the convergents of $\sqrt{2}$ , the $+1$-case is the well known Pell-equation, the $-1$-case an also well known variant. – Peter Aug 02 '18 at 11:57