  We compute the ring of non-induced representations for a cyclic group, $C_n$,
over an arbitrary field and show that it has rank $\varphi(n)$, where $\varphi$
is Euler's totient function - independent of the characteristic of the field.
Along the way, we obtain a "pick-a-number" trick; expressing an integer $n$ as
a sum of products of $p$-adic digits of related integers.
