Jacobsthal identity for Q(sqrt(-2))

Details Jacobsthal identity for Q(sqrt(-2)) Jacobsthal identity for Q(sqrt(-2))

2011-10-26

arxiv.org/abs/1110.5815v1

Mathematics

Number Theory

to appear in Forum Mathematicum

Scientific paper

10.1515/FORM.2011.102

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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