MathNet 2015-part-07 — 185 problems (EN–VI) Question 34

Let $N = 30^{2015}$. Find the number of ordered 4-tuples of integers $(A, B, C, D) \in \{1, 2, \ldots, N\}^4$ (not necessarily distinct) such that for every integer $n$, $A n^3 + B n^2 + 2 C n + D$ is divisible by $N$.