Jacobsthal identity for Q(√ - 2)

Ki Ichiro Hashimoto*, Ling Long, Yifan Yang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Let p be a prime congruent to 1 or 3 modulo 8 so that the equation p = a 2 C 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.

Original languageEnglish
Pages (from-to)1225-1238
Number of pages14
JournalForum Mathematicum
Issue number6
Publication statusPublished - 2012 Nov 1


  • Hyperelliptic curve
  • Jacobsthal sum
  • L-function

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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