1984 USAMO Problems/Problem 5

Problem

$P(x)$ 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 $n$ .

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1984 USAMO (Problems • Resources)
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1984 USAMO Problems/Problem 5

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