  We study monogeneity in {\sl period equations}, $\psi_e(x)$, the auxiliary
equations introduced by Gauss to solve cyclotomic polynomials by radicals. All
monogenic $\psi_e(x)$ of degrees $4 \leq e \leq 250$ are determined for
extended intervals of primes $p=ef+1$, and found to coincide either with
cyclotomic polynomials, or with simple de Moivre reduced forms of cyclotomic
polynomials. The former case occurs for $p=e+1$, and the latter for $p=2e+1$.
For $e\geq4$, we conjecture all monogenic period equations to be cyclotomic
polynomials. Totally real period equations are of interest in applications of
quadratic discrete-time dynamical systems.
