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Number theory

Source: Polish National Olympiad 2015 2nd round, 3rd problem

March 3, 2015
number theory

Problem Statement

Let an=∣n(n+1)−19∣a_{n}=|n(n+1)-19| for n=0,1,2,...n=0, 1, 2, ... and n≠4n \neq 4. Prove that if for every k<nk<n we have gcd⁡(an,ak)=1\gcd(a_{n}, a_{k})=1, then ana_{n} is a prime number.
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