#1**+1 **

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

HighSchoolDx May 16, 2021