algebra precalculus - Showing that $forall ain mathbb Z exists b in mathbb Z$ such that $ab+1$ is perfect square

first time asking a question here.

This proof seems simple, but the only part throwing me off is the the first two remarks
"Show that for every positive integer a, there exist a positive integer $b$ such that $ab+1$ is a perfect square."

What I have is:
Let $k = n^2$ where is an integer and $n^2$ is perfect square.
then $ab+ 1 = k$

This is where I get stuck.