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The equation $ax^2 +by^2 =1 \mod P$ in cyclotomic field

Let $L$ be a cyclotomic field, and $P$ a prime ideal of $\mathcal{O}_L$. is there any symbol for the equation $ax^2 + by^2 =1 \mod P$ and if so, is it computable in polynomial time? if $a$ is ...
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