I’m currently studying equations over finite fields (in particular solutions over $F\_{q^k}$ to equations of the form $y^q-y=f(X)$ for a polynomial $f(X) \in F\_q[X]$) and approximations of the number of their solutions.  

In the above case (with N being the number of solutions $(x,y) \in (F\_{q^k})^2$ to $y^q-y=f(X)$) we know that $|N-q^k|<q^{[\frac{k}{2}]+4}$.

I am wondering now, how those results, that we find, can be applied (e.g. in computer science). Why are we even studying those equations? Can someone provide me with an example of an application?

Thank you a lot in advance!