Divisiblity of $n$ with $a,b,c$ is relative prime to p

Question

Given an arbitrary prime $p > 2011$. Prove that there exist positive integers $a,b,c$ such that there exists some numbers from $a, b, c$ that are relatively prime to $p$, and for all positive integers $n$ such that $p|n^4 − 2n^2 + 9$, $p$ divides $24an^2 + 5bn + 2011c$.

I have no idea for this problem

Answer 1

Choose $a,b,c$ such that: $p| 24a-1 ; p| 5b+2; p|2011c-9$