Corollary 2 Under the notation and conditions of Theorem 1, we have
(i) When $l$ is even, the indeterminate equation (2) has no solution, and all solutions of the indeterminate equation (1) are
$$x= \pm h_{l j-1}, \quad y= \pm k_{l j-1}, \quad j=0,1,2, \cdots,$$

where the signs are chosen arbitrarily.
(ii) When $l$ is odd, all solutions of the indeterminate equation (2) are
$$x= \pm h_{l j-1}, \quad y= \pm k_{l j-1}, \quad j=1,3,5, \cdots$$

and all solutions of the indeterminate equation (1) are
$$x= \pm h_{l j-1}, \quad y= \pm k_{l j-1}, \quad j=0,2,4, \cdots,$$
where the signs are chosen arbitrarily.