Problem

Source: USAMO 1984 Problem 5

Tags: AMC, USA(J)MO, USAMO, algebra, polynomial, geometry, 3D geometry



$P(x)$ is a polynomial of degree $3n$ such that \begin{eqnarray*} P(0) = P(3) = \cdots &=& P(3n) = 2, \\ P(1) = P(4) = \cdots &=& P(3n-2) = 1, \\ P(2) = P(5) = \cdots &=& P(3n-1) = 0, \quad\text{ and }\\ && P(3n+1) = 730.\end{eqnarray*} Determine $n$.