Roots of unity and nullity modulo $n$
Roots of unity and nullity modulo $n$
For a fixed positive integer $\ell$, we consider the function of $n$ that counts the number of elements of order $\ell$ in $\mathbb {Z}_n^*$. We show that the average growth rate of this function is $C_\ell (\log n)^{d(\ell )-1}$ for an explicitly given constant $C_\ell$, where $d(\ell )$ is the …