关于不定方程x^2-5ly^2=1与y^2-Dz^2=49的公解

On the Simultaneous Indefinite Equationsx^2-51y^2=1 and y^2-Dz^2=49

设ps（1≤s≤4）是互异的奇素数，D=2tp1a1p2a2p3a3p3a4p4a4（ai=0或1，1≤i≤4，t∈Z＋）时，不定方程x2-51y2=y2-Dz2=49仅当D=2t×4999（t=1，3，5）时有非平凡公解（x，y，z）=（±50，±7，0）．

Let D=2tp1a1p2a2p3a3p3a4p4a4（ai=0 or 1,1≤i≤4,t∈Z＋）时, where are distinct odd primes, the simultaneous Diophantine equations in the title has a positive integer solution only when D = 2t × 4999 （t = 1, 3, 5）.