**Goal:**

We look at solutions of polynomial equations f(x,y)=0 over
finite fields and try to discover patterns in the number of such solutions.
In fact, we are counting points on curves over finite fields.
With little experimenting very quickly you will see
some patterns arising.
Prerequisites are that you know what a finite field is and
that you are willing to experiment to find
the number of solutions with a computer (or even by hand if you
have enough perseverance). Once you see some patterns
appear the successive experiments will present themselves.
The project file suggests step by step what
experiment to do. At the end you know what to do.

**Supervisors:**
Gerard van der Geer, Bryan Advocaat

**Difficulty level:**
Any

**Tools:**
Any programming language or any Computer Algebra System

**Bibliography:**
Upon request