Plane algebraic curve/Circle equation/Points over finite field/K is F 2, F 3, F 5, F 7/Exercise

Determine all solutions of the circle equation

${}x^{2}+y^{2}=1\,$

for the fields ${}K=\mathbb {Z} /(2)$, ${}\mathbb {Z} /(3)$, ${}\mathbb {Z} /(5)$, and ${}\mathbb {Z} /(7)$.

Create a solution