VTMO 2017 — Grade 8 — final Question 1

$a$)Find the smallest positive $n$ such that $\left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(n + 4\right)$ is divisible by $1000$. $b$)Prove a $^{4} + 324 b^{4}$ is not prime for positive integers $a , b$.