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arXiv · 1110.5815

Jacobsthal identity for Q(sqrt(-2))

Ki-Ichiro Hashimoto·Ling Long·Yifan Yang
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Abstract

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 of Jacobsthal sums. This is analogous to a classical identity of Jacobsthal.

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Ki-Ichiro Hashimoto, Ling Long, Yifan Yang. 2011-10-26. Jacobsthal identity for Q(sqrt(-2)). https://doi.org/10.1515/form.2011.102

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