This is Theorem 2.3.8 from Scharlau's book Quadratic and Hermitian Forms So basically I know that since $\mathbb{F}_q$/$\mathbb{F}_q^2$ has index 2; it represent 2 classes. One class represents elements which are sqaures and other class represent non-squares.Only problem seems to me in this proof is second line which says that every element of $\mathbb{F}_q$ is sum of two squares implies $\langle 1,1\rangle$ represents $\epsilon$? What is meaning of this notation?