Show that every nonzero integer can be uniquely represented in the form $$ e_{k} 3^{k}+e_{k-1} 3^{k-1}+\cdots+e_{1} 3+e_{0} $$ where $e_{j}=-1,0$ or 1 for $j=0,1,2, \ldots, k$ and $e_{k} \neq 0$. This expansion is called a balanced ternary expansion.