[Hints] 2016 Canadian Math Olympiad Problem 3

2016 Canada MO 3. Find all polynomials P(x) with integer coefficients such that P(P(n) + n) is a prime number for infinitely many integers n.

Hint 1: Work out the cases where the degree of the polynomial P is 0 or 1. Are there any solutions here?

Scroll down for hint 2…

 

 

 

 

 

 

 

 

 

Hint 2: Use the lemma a - b \mid P(a) - P(b) to show that P(P(n) + n) always has a factor.

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