8 - Motivating Motives previous next

Let's count the number of solutions of $$ y^2 + y = x^3 + x $$ over the finite field with q = pn elements, called \(\mathbb{F}_q\). Take p = 2:

n   q = pn   number of solutions
1 2 4
2 4 4
3 8 4
4 16 24
5 32 24
6 64 64
7 128 144
8 256 224
9 512 544
10 1024 1024