Q:

Find all integer numbers $n$ such that $\frac{11n-5}{n+4}$ is a perfect square. 

Find all integer numbers $n$, such that, $$\sqrt{\frac{11n-5}{n+4}}\in \mathbb{N}$$
I really tried but I couldn't guys, help please. 

A:

If our square root is to be an integer, we need to have $\frac{11n-5}{n+4}$ a non-negative integer.  Note that
$$\frac{11n-5}{n+4}=11-\frac{49}{n+4}.$$
So $n+4$ must divide $49$. But $49$ has very few divisors, so there are very few possile integer values of $\frac{49}{n+4}$. Try them all, including the negative ones.  For each candidate, check whether the number $11-\frac{49}{n+4}$ is a perfect square. 