The pell equation x 2-py 2 = 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 = k 2. In this paper, we consider the integer solutions of the Pell equation x 2-Py 2 = Q over Z and also over finite fields F p. Also we deduce some relations on the integer solutions (x n, y n) of it.