\(2015=5.13.31\)
Ta có: \(1.2.....1007=1.2...5....13.....31...1007\text{ chia hết cho }5.13.31=2015\)
\(1008.1009.....2004=1008....\left(1010\right)....\left(1014\right)...\left(1023\right)....2004\)
\(=1008....\left(5.202\right)....\left(13.78\right)....\left(31.33\right)...2004\text{ chia hết cho }5.13.33=2015\)
Do đó tổng 2 số trên chia hết cho 2015.