# The Biggest Degree

Algebra Level 4

Find the largest possible degree $n \le 1000$ of a polynomial $p(x)$ such that

1. $p(i) = i \,$ for every integer $i$ with $1 \le i \leq n;$
2. $p(-1) = 1671;$
3. $p(0)$ is an integer (not necessarily 0).
×