The Pell equation x2 - Py2 = Q

Abstract

Let p be a prime number such that p =1(mod 4), say p =1+4k for a positive integer k. Let P =2k +1 and Q = k2. In this paper, we consider the integer solutions of the Pell equation x2-Py2 = Q over Z and also over finite fields Fp. Also we deduce some relations on the integer solutions (xn,yn) of it.