14. A Cantor expansion of a positive integer $n$ is a sum
$$n=a_{m} m!+a_{m-1}(m-1)!+\cdots+a_{2} 2!+a_{1} 1!$$
where each $a_{j}$ is an integer with $0 \leqslant a_{j} \leqslant j$.
a) Find Cantor expansions of 14,56 , and 384 .
b) Show that every positive integer has a unique Cantor expansion.
14. а) $14=2 \cdot 3!+1 \cdot 2!, 56=2 \cdot 4!+1 \cdot 3!+1 \cdot 2!, 384=3 \cdot 5!+1 \cdot 4$ !