find all positive integer $n$, satisfying $$\frac{n(n+2016)(n+2\cdot 2016)(n+3\cdot 2016) . . . (n+2015\cdot 2016)}{1\cdot 2 \cdot 3 \cdot . . . . . \cdot 2016}$$is positive integer.
Source: 2016 KJMO #4
Tags: number theory
find all positive integer $n$, satisfying $$\frac{n(n+2016)(n+2\cdot 2016)(n+3\cdot 2016) . . . (n+2015\cdot 2016)}{1\cdot 2 \cdot 3 \cdot . . . . . \cdot 2016}$$is positive integer.