二次域Q（√p）中的完全平方数
Complete Square Number in Real Quadratic Fields of Q (√p)
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摘要: 运用Pell方程的知识，借助于不定方程的解题方法，二次域Q（√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^2+-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.Abstract: 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= (d) are presented. It is proved that, for any prime numberp, there exists an infinite number of complete squares in the form of py2±1, which further proves that, for any square-free numberp , there also exists an infinite number of complete squares in the form of dy2+1
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