二次域 （√P）中的完全平方数

摘要

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）rnare 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%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）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py^z±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dy^2＋1的完全平方数．