关于Pell方程x^2-Dy^2=-1的一个注记

A Note on the Pell Equation x^2-Dy^2=-1

设pi≡5(mod 8)(i=1,2,…,s)为不同的奇质数,D=2p_1…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x^2-Dy^2=-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x^2-Dy^2=-1的有解判别.

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 x^2-Dy^2= 1,in [1],some criterions for the solvability of the Pell equation x^2-Dy^2=-1 are obtained when s2. 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 x^2-Dy^2=-1 when s = 1,2.