PAMO 2016 Problem 3

For any positive integer $n$ , we define the integer $P(n)$ by : $P(n)=n(n+1)(2n+1)(3n+1)...(16n+1)$ .

Find the greatest common divisor of the integers $P(1)$ , $P(2)$ , $P(3),...,P(2016)$ .