Question 95
Let $a_1 \lt a_2 \lt a_3 \lt \dots$ be positive integers such that $a_{k+1}$ divides $2(a_1 + a_2 + \dots + a_k)$ for every $k \ge 1$. Suppose that for infinitely many primes $p$, there exists $k$ such that $p$ divides $a_k$. Prove that for every positive integer $n$, there exists $k$ such that $n$ divides $a_k$.