2016 Pan-African Math Olympiad Problem 3

2016 PAMO 3. For any positive integer n, we define the integer P(n) as

P(n) = n(n+1)(2n+1)(3n+1) \dots (16n + 1).

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

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