Definition (e(x)). Let $x\in \mathbb{N}$ and $p$ a prime. Then we can write

$$x=a_k{p}^k+\cdots +a_{1}p+a_0,$$

with $0\le a_i<p$. Denote by $e(x)=\{a_t:t=\min ,cbi:a_i\ne 0\}$.