[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?

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