RESEARCH ANNOUNCEMENTSOn the Simultaneous Pell Equations x~2-D_(1y)~2=δ and z~2 - D_(2y)~2 =δ

Let Z, N, Q be the sets of all integers, positive integers and rational numbers, respectively.Let D1, D2 be distinct positive integers, and let . The simultaneous Pell equationsarise in connection with a variety of classical problems on number theory and arithmetic algebraicgeometry. As has been noted by K. One1], the solutions (x, y, z) of (1) imply the existence ofrational points of infinite order on the elliptic curveLet p, q be twin primes withRecently, Qiu Derong and Zhang Xianke2…