We say that a triple of integers $(x, y, z)$ is of jenifer type if $x, y$, and $z$ are positive integers, with $y \ge 2$, and $$x^2 - 3y^2 = z^2 - 3.$$a) Find a triple $(x, y, z)$ of the jenifer type with $x = 5$ and $x = 7$. b) Show that for every $x \ge 5$ and odd there are at least two distinct triples $(x, y_1, z_1)$ and $(x, y_2, z_2)$ of jenifer type. c) Find some triple $(x, y, z)$ of jenifer type with $x$ even.