Hi everybody. I'd like to know if the diophantine equation

$$X^2 - Y^2 - Z^2 = \pm 1$$

has been studied and if the set of its solutions $(X,Y,Z)$ is known. I appreciate any reference. Thank you very much.

Hi everybody. I'd like to know if the diophantine equation

(1) $$X^2 - Y^2 - Z^2 = \pm 1$$

has been studied and if the set of its solutions $(X,Y,Z)$ is known. I appreciate any reference. Thank you very much.

P.S. If instead we look at the diophantine equation

$$X^2 - Y^2 - Z^4 = \pm 1$$

surely we can solve it imposing conditions on the solution of (1) so that Z be a square. However, is there a quicker method?