$a_0+a_1p^1+..+a_kp^{k}=b_0+b_1p^1+..+b_kp^{k}$ imply $\forall\ 0\le i \le k\ a_i=b_i$; $p$ is prime, $\forall\ 0\le i \le k: 0\le a_i,b_i<p$
Prove that there is only one unique base b representation of any natural number.