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USAMO 1984 Problem 5

  • Day 2
  • Answer

A polynomial of degree 3n3 n has the value 2 at 0,3,6,…,3n0,3,6, \ldots, 3 n, the value 1 at 1,4,7,…,3n−21,4,7, \ldots, 3 n-2 and the value 0 at 2,5,8,…,3n−12,5,8, \ldots, 3 n-1. Its value at 3n+13 n+1 is 730 . What is nn ?

Dataset text NuminaMath olympiads. Quoted with source.

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