On the number of solutions to systems of Pell equations Original Research Article

We prove that, for positive integers a, b, c and d with c≠d, a>1, b>1, the number of simultaneous solutions in positive integers to ax2−cz2=1, by2−dz2=1 is at most two. This result is the best possible one. We prove a similar result for the system of equations x2−ay2=1, z2−bx2=1.