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5

Part of 1984 USAMO

Problems(1)

USAMO 1984 Problem 5 - Polynomial of degree 3n

Source: USAMO 1984 Problem 5

8/16/2011
P(x)P(x) is a polynomial of degree 3n3n 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 nn.
AMCUSA(J)MOUSAMOalgebrapolynomialgeometry3D geometry