关于不定方程x^2-23y^2=1与y^2-Dz^2=25的公解

On the Simultaneous Indefinite Equationsx^2-23y^2=1 and y^2-Dz^2=25

设Ps（1≤s≤4）是互异的奇素数，D=2^tp1^a1p2^a2p3^a3p4^a4（ai=0或1，1≤i≤4，t∈Z^＋）时，不定方程x^2-23y^2=1与y^2-Dz^2=25仅当D=2^t×1151（t=1，3，5，7，9）时有正整数解．

Let D=2^tp1^a1p2^a2p3^a3p4^a4 （ai=0 or 1,1≤i≤4,t∈Z^＋）,where ps（1≤s≤4）are distinct odd primes, the simultaneous Diophantine equations in the title has a positive integer solution only when D = 2^t × 1151 （t = 1, 3, 5, 7, 9）.