periodicity of constant discrete time signals
normally, "$n$" is the symbol we use here for discrete-time.  if your professor said that:

$$\begin{align}
x[n] &amp;= e^{i10 \pi n} \\
 &amp;= e^{i 2 \pi (5n)} \\
\end{align}$$

is not periodic with a period of $1$ (assuming $n \in \mathbb{Z}$) or a period of $\frac15$ (assuming $n \in \mathbb{R}$), then your professor is mistaken.