For positive integer $k$, let $M = 2(2k-1)$, which of the following must be true?
(a) $M$ is not a perfect square for any $k$.
(b) There are infinitely many $k$ such that $M$ is a perfect square.
(c) There is a unique $k$ such that $M$ is a perfect square.
(d) There are finitely many, but more than 1, values of $k$ such that $M$ is a perfect square.
This question was on my Math Challenge II Number Theory packet. I'd also like a proof of how you got your answer.