Let
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
be a positive integer. Show that there are infinitely many perfect squares of the form
![n \cdot 2^k - 7](/media/m/9/d/e/9deec60200a177393ac9ad3ef02f4eb5.png)
where
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
is a positive integer.
%V0
Let $k$ be a positive integer. Show that there are infinitely many perfect squares of the form $n \cdot 2^k - 7$ where $n$ is a positive integer.