TITLE: Solution of a system of equations in a finite field using Mathematica
QUESTION [6 upvotes]: We can solve a system of equations over reals using Mathematica as follows.
Solve [x^2+y^2+z^2==1 && x+y==1, {x,y,z}]

How one can solve a system of equations over a finite field like GF(2) using Mathematica?

REPLY [8 votes]: Solve[x^2+y^2+z^2==1 && x+y==1, {x,y,z}, Modulus->2]