Jacobsthal identity for Q(sqrt(-2))

Ki-Ichiro Hashimoto, Ling Long, Yifan Yang

Let $p$ be a prime congruent to 1 or 3 modulo 8 so that the equation $p=a^2+2b^2$ is solvable in integers. In this paper, we obtain closed-form expressions for $a$ and $b$ in terms…