The fundamental solution of $x^2 - Dy^2 = -1$, say $(x_0, y_0)$, satisfies $x_0^2 + Dy_0^2 = 1$

If $(x_1, y_1)$ is the fundamental solution of $x^2 - Dy^2 = -1$, then $(x_1^2 + Dy_1^2, 2x_1y_1)$ is the fundamental solution of $x^2 - Dy^2 = 1$

The negative Pell equation always has solutions for any square-free $D > 0$

The solutions of the negative Pell equation are always a subset of the positive Pell equation