\begin{definition}[Definition:Balanced Ternary Representation]
Let $n \in \Z$ be an integer.
'''Balanced ternary representation''' is the unique representation of $n$ in the form:
:$\sqbrk {r_m r_{m - 1} \ldots r_2 r_1 r_0}$
such that:
:$\ds n = \sum_{j \mathop = 0}^m r_j 3^j$
where:
:$m \in \Z_{>0}$ is a strictly positive integer such that $3^m \le \size n < 3^{m + 1}$
:all the $r_j$ are such that $r_j \in \set {\underline 1, 0, 1}$, where $\underline 1 := -1$.
\end{definition}