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Let the $X = \{1,2,\ldots,2000\}$. How many subsets $T$ of $X$ are such that the sum of the elements of $T$ is divisible by 5?

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    What do you mean the sum contains 5? Presumably you don't mean just $\{1,4\}$ and $\{2,3\}$.2012-12-05
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    for example one subset is $\left \{1;2;3;4 \right \}$ and $1+2+3+4=10$ divisible for 5, if you understand my meanings can you edit my words, sorry about my bad english2012-12-05
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    ok, I have the result that $\frac{1}{5}(2^{402}+2^{2000})$ but I don't have the solution, any one can help me2012-12-06

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