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Let S = 1 + 2 + 3 + ... + 2010. What is the residue of S, modulo 2010?

 Jul 28, 2021
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This is $\frac{2010\cdot 2011}{2}$, which is an odd multiple of $1005$, hence it's residue is $1005$.

 Jul 28, 2021

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