Number of roots of unity in a finite cyclic group G, source to cite

Question

Can anybody point me to an official book or paper that has a complete proof to the statement

In a finite cyclic group $G$ then number of solutions to $x^n = 1$ is $\gcd(n,|G|)$

I have pieced together a proof using other stack exchange post but want to use an official reference to cite in my bachelor thesis.

Thanks a lot