Question 71
Find all prime numbers $p$ for which one can find a positive integer $m$ and non-negative integers $a_0, a_1, \dots, a_m$ less than $p$ such that
$$
\begin{cases} a_0 + a_1 p + \dots + a_{m-1} p^{m-1} + a_m p^m = 2013, \\ a_0 + a_1 + \dots + a_{m-1} + a_m = 11. \end{cases}
$$
$$
\begin{cases} a_0 + a_1 p + \dots + a_{m-1} p^{m-1} + a_m p^m = 2013, \\ a_0 + a_1 + \dots + a_{m-1} + a_m = 11. \end{cases}
$$