BG-MO 2001 Problem 3

Let $p$ be a prime number congruent to $3$ modulo $4$ , and consider the equation $(p+2)x^{2}-(p+1)y^{2}+px+(p+2)y=1$ . Prove that this equation has infinitely many solutions in positive integers, and show that if $(x,y) = (x_{0}, y_{0})$ is a solution of the equation in positive integers, then $p | x_{0}$ .