二次域■(p～(1/2))中的完全平方数

Complete Square Number in Real Quadratic Fields of ■(p～(1/2)

运用Pell方程的知识,借助于不定方程的解题方法,对二次域■(p～(1/2)的基本单位的范进行研究.给出了Pell方程的解,并证明了对于任意素数p,存在无穷多个形如py2±1的完全平方数,进一步说明了对于任意无平方因子数d,存在着无穷多个形如dy2+1的完全平方数.

Norm, the basic unit in the quadratic field of （√P）, is studied by application of the solution approach in solving Diophantine equations and the knowledge of Pell equation and then the solutions of Pell equation in K= （√P） are presented. It is proved that, for any prime numherp, there exists an infinite number of complete squares in the form of py^2 ±1, which further proves that, for any square-free numberp , there also exists an infinite number of complete squares in the form of dy^2 ＋ 1