Difference between revisions of "1984 USAMO Problems/Problem 5"

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Determine <math>n</math>.
 
Determine <math>n</math>.
  
== Solution ==
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== Solution ==gg
  
 
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Revision as of 16:25, 30 November 2016

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 $n$.

== Solution ==gg

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See Also

1984 USAMO (ProblemsResources)
Preceded by
Problem 4
Followed by
Last Question
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All USAMO Problems and Solutions

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