Pell's equation (simple solutions)

Pell's equation is any Diophantine equation of the form where is a given positive nonsquare integer, and integer solutions are sought for and

Denote the sequence of solutions {x_i, y_i}. It is clear that {x_0, y_0} = {1,0}. During the solution we need: a) to construct a recurrent sequence {x_{i+1}, y_{i+1}} = f({x_i, y_i}) or two sequences {x_{i+1}} = f({x_i}), {y_{ i+1}} = g({y_i}); b) to prove that the equation has no other integer solutions.