A Counting Proof for When 2 Is a Quadratic Residue

Abstract

Using the group consisting of the eight Möbius transformations x, – x, 1/x,−1/x, (x−1)/(x+1),(x+1)/(1−x), (x+1)/(x−1), and (1−x)/(x+1), we present an enumerative proof of the classical result for when the element 2 is a quadratic residue in the finite field Fq .