English

Jacobsthal identity for Q(sqrt(-2))

Number Theory 2011-10-27 v1

Abstract

Let pp be a prime congruent to 1 or 3 modulo 8 so that the equation p=a2+2b2p=a^2+2b^2 is solvable in integers. In this paper, we obtain closed-form expressions for aa and bb in terms of Jacobsthal sums. This is analogous to a classical identity of Jacobsthal.

Keywords

Cite

@article{arxiv.1110.5815,
  title  = {Jacobsthal identity for Q(sqrt(-2))},
  author = {Ki-Ichiro Hashimoto and Ling Long and Yifan Yang},
  journal= {arXiv preprint arXiv:1110.5815},
  year   = {2011}
}

Comments

to appear in Forum Mathematicum

R2 v1 2026-06-21T19:26:08.007Z