关于Diophantine方程x^2+py^2=(p+1)z^2

On the Diophantine equation x^2+py^2=(p+1)z^2

利用初等的方法,研究p=1,2,4时,不定方程x^2+py^2=(p+1)z^2的解,给出了解的一般结构,这在实际应用中有广泛的作用,并给出了一些特殊解.在此基础上,给出不定方程x^2+py^2=(p+1)z^2求解问题一个切实有效的方法.

By using the elementary method,the solution of Diophantine equation x^2+py^2=(p+1)z^2 at p=1,2,4 is studied,the general structure of the solution is given,which is widely used in the practical application,and some special solutions are given.On this basis,a practical and effective method for solving Diophantine equations x^2+py^2=(p+1)z^2 is given.