USAMO 1984 Problem 5 - Polynomial of degree 3n
Source: USAMO 1984 Problem 5
August 16, 2011
AMCUSA(J)MOUSAMOalgebrapolynomialgeometry3D geometry
Problem Statement
is a polynomial of degree 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, \text{ and }\\
&& P(3n+1) = 730.\end{eqnarray*}Determine .