Prove that there are infinitely many positive integers
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
such that
![n^{2} + 1](/media/m/0/f/7/0f776b362eae73c86741905d550ab0cd.png)
has a prime divisor greater than
![2n + \sqrt {2n}](/media/m/3/3/2/3329f5a6d85fe4218f90a3a499efee5f.png)
.
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