Complete Square Number in Real Quadratic Fields of Q (√p)

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