【摘要】 设D=2p₁···p_s（1≤s≤4），其中p₁，···，p_s是互不相同的奇素数。主要利用奇偶分析、同余、递归序列以及Pell方程解的性质等初等方法，对Pell方程组x²-40y²=1与y²-Dz²=9的公解进行研究。得出当D≠2×7×103时，该方程组仅有平凡解（x,y,z）=（±19，±3,0）；当D=2×7×103时，除了平凡解（x,y,z）=（±19，±3,0）外，还有非平凡解（x,y,z）=（±27 379，±4 329，±114）。研究结果丰富了这类Pell方程组整数解的研究内容。更多还原

【Abstract】 Let D = 2p₁···ps（1 ≤ s ≤ 4）, where p1,···,ps are distinct odd prime numbers. The common solutions of Pell equations x²-40y²= 1 and y²-Dz²= 9 are studied by using parity analysis, congruence, recursive sequence and properties of the solutions of Pell equations. It is concluded that when D ≠ 2 × 7 × 103, the system have only trivial solution（x,y,z） =（±19,±3,0）;when D = 2 × 7 × 103, in addition to the trivial solution（x,y,z） =（±19,±3,0）, there is non-trivial solution（x,y,z） =（±27 379,±4 329,±114）. The results enrich the research content of the integer solution of this kind of Pell equations.更多还原