Question 72
Let $a_1, a_2, \dots, a_{1000}$ be a sequence of integers such that $a_1 = 3$, $a_2 = 7$ and for all $n = 2, 3, \dots, 999$
$$
a_{n+1} - a_n = 4(a_1 + a_2)(a_2 + a_3) \cdots (a_{n-1} + a_n).
$$
Find the number of indices $1 \le n \le 1000$ for which $a_n + 2018$ is a perfect square.
$$
a_{n+1} - a_n = 4(a_1 + a_2)(a_2 + a_3) \cdots (a_{n-1} + a_n).
$$
Find the number of indices $1 \le n \le 1000$ for which $a_n + 2018$ is a perfect square.