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

 May 16, 2021
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the sum can be expressed as 2011 * 1005. Then, we know that 2010 * 1005 is a multiple of 2010. adding 1005 onto that then it is 2011 * 1005, which is S. I am not familiar with residues, but I do knowk that S mod 2010 = 1005 hope this helps

 May 16, 2021

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