Problem - 3070
If $2016$ consecutive integers are added together, where the $999^{th}$ number in the sequence is $1,244,584$, what is the remainder when this sum is divided by $6$?
Answer
0
Because $2016$ is a multiple of $6$, therefore, the remainders of the sum of these numbers divides $6$ will equal $$(0+1+2+\cdots+5) \times 2016 / 6\equiv \boxed{0}\pmod{6}$$