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Omni-MATH / P(x) is a polynomial of degree 3n such that

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problem

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, \quad\text{ and }\\ && P(3n+1) = 730.\end{eqnarray*} Determine nn .
Plain-text mathematical notation (without MathML)
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 .
Original LaTeX notation
$P(x)$ 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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task_id
fbb9c8f2-51c6-59f7-b39f-edb31358f688
task_key
test--fbb9c8f2-51c6-59f7-b39f-edb31358f688
task_revision_id
1
config / split
/ test

Official source

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