Problem

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2019 3.5

Tags: number theory, divides



We have an a sequence such that $a_n = 2 \cdot 10^{n + 1} + 19$. Determine all the primes $p$, with $p \le 19$, for which there exists some $n \ge 1$ such that $p$ divides $a_n$.