Tag Archives: totient

The multiplicative group of a finite field is cyclic

Today, we are going to prove that if $F$ is a finite field, the the multiplicative group $F^\times$ of $F$ is a cyclic group. Let’s start with an example of this phenomenon. Take $\F_5 = \{0,1,2,3,4\}$. Now, if we take powers of $2$ modulo $5$ we get $$2,2^2=4,2^3 = 3, 2^4 = 1.$$ Therefore, we […]