Prove that there are infinitely many positive integers such that has a prime divisor greater than .
Author: Kestutis Cesnavicius, Lithuania
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Prove that there are infinitely many positive integers $n$ such that $n^{2} + 1$ has a prime divisor greater than $2n + \sqrt {2n}$.
Author: Kestutis Cesnavicius, Lithuania
Source: Međunarodna matematička olimpijada, shortlist 2008
Školjka 
such that 
has a prime divisor greater than 
.