English

On non-congruent numbers with 1 modulo 4 prime factors

Number Theory 2012-08-13 v1

Abstract

In this paper, we use the 2-decent method to find a series of odd non-congruent numbers 1(mod8)\equiv1\pmod 8 whose prime factors are 1(mod4)\equiv1\pmod4 such that the congruent elliptic curves have second lowest Selmer groups, which includes Li and Tian's result (Li and Tian, 2000) as special cases.

Keywords

Cite

@article{arxiv.1208.2149,
  title  = {On non-congruent numbers with 1 modulo 4 prime factors},
  author = {Yi Ouyang and Shenxing Zhang},
  journal= {arXiv preprint arXiv:1208.2149},
  year   = {2012}
}