Let $N = \frac{3k−8}{k+4}$,
where $k$ is an integer.
List all positive values of k for which $N$ is an integer.
Do this using algebra, without using a calculator.
Also do not do this by enumeration, i.e., plugging in $k = 1, 2, ...$ and checking the value of $N$.
The hint: $$\frac{3k-8}{k+4}=\frac{3k+12-20}{k+4}=3-\frac{20}{k+4},$$ which says that $20$ is divisible by $k+4$.
Id est, $$k+4\in\{5,10,20\}$$ because $k>0$