LIAO Qun-ying,ZHANG Song,HE Qing-yun,et al.A Note on the Pell Equation x2-Dy2=-1[J].Journal of Chengdu University of Information Technology,2017,(03):341-342.[doi:10.16836/j.cnki.jcuit.2017.03.017]
关于Pell方程x2-Dy2=-1的一个注记
- Title:
- A Note on the Pell Equation x2-Dy2=-1
- 文章编号:
- 2096-1618(2017)03-0341-02
- 关键词:
- Pell方程; 基本解; Legendre符号
- Keywords:
- Pell equation; elementary solution; Legendre symbol
- 分类号:
- O156.4
- 文献标志码:
- A
- 摘要:
- 设pi≡5(mod 8)(i=1,2,…,s)为不同的奇质数,D=2p1…ps.利用方程x2-Dy2=1的基本解的性质,文献[1]给出s>2时,Pell方程x2-Dy2=-1的有解判别条件.为进一步研究该问题,利用初等的方法和技巧,完善了上述结果:即给出s=1,2时,方程x2-Dy2=-1的有解判别.
- Abstract:
- Let pi≡5(mod 8)(i=1,2,…,s)be distinct primes and D=2p1…,ps.Based on properties for the elementary solutions of the Pell equation x2-Dy2=1,in [1],some criterions for the solvability of the Pell equation x2-Dy2=-1 are obtained when s>2. Based on elementary methods and techniques, the present paper continues the study and improves the results, namely, obtains a criterions for the solvability of the Pell equation x2-Dy2=-1 when s=1,2.
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备注/Memo
收稿日期:2017-03-27 基金项目:国家自然科学基金资助项目(11401408); 四川省科技厅科研重点资助项目(2016JY0134)