  We provide an equivalent condition for the monogenity of the ring of integers
of any cyclic cubic field. We show that if a cyclic cubic field is monogenic
then it is a simplest cubic field $K_t$ which is the splitting field of a
Shanks cubic polynomial $f_t(x):=x^3-tx^2-(t + 3)x-1$ with $t \in \mathbb Z$.
Moreover we give an equivalent condition for when $K_t$ is monogenic, which is
explicitly written in terms of $t$.

Number Theory