Consider the quadratic Diophantine equation $x^2 - 6xy + y^2 = 1$. Which statement best describes the solution set?

(A) The equation has no integer solutions except $(\pm 1, 0)$ and $(0, \pm 1)$.

(B) The equation has infinitely many integer solutions that can be generated from a finite set of fundamental solutions.

(C) The equation has exactly four solutions: $(1, 0), (-1, 0), (0, 1), (0, -1)$.

(D) The equation is equivalent to a Pell equation and has a single fundamental solution generating all others.