## [Hints] 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 $P(1), P(2), P(3), \dots, P(2016)$.

Hint 1: Let $G$ be the greatest common divisor desired. What are the possible primes in $G$‘s prime factorisation?

Hint 2: Is 2 a divisor of $P(1), P(2), \dots, P(2016)$? How about 4? Can this argument be extended to the other primes that could be in $G$‘s prime factorisation?