N=2013x10^(2012x4)+2013x10^(2011x4)+...+2013x10^4+2013x10^0
N mod(1001)=>11x10^(2012x4)+11x10^(2011x4)+...+11x10^0
=>1111x10^(2011x4)+1111x10^(2009x4)+...+1111x10^1+11
=>110x10^(2011x3)+110x10^(2009x3)+...+110x10^1+11
=>110110x10^(2009x6)+110110x10^(2007x6)+...+110110x10^1+11
=>0 + 11
=>11
110110 is multiple of 1001