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1 \binom{2008}{0 }+2\binom{2008}{1}+ ...+2009\binom{2008}{2008} mod2008

Source: Austrian Federal Competition For Advanced Students 2008, Part 1, p1

August 30, 2019
number theorybinomial coefficientsDivisibility

Problem Statement

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?
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