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AT-OEMO-FED1 2008 Problem 1

    What is the remainder of the number 1(20080)+2(20081)+...+2009(20082008)1 \binom{2008}{0 }+2\binom{2008}{1}+ ...+2009\binom{2008}{2008} when divided by 20082008 ?

    Dataset text AI-MO AoPS. Quoted with source.

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