Largest Prime Factor of n squared plus 1

Theorem
Let $n \in \Z$ be greater than $239$.

Then the largest prime factor of $n^2 + 1$ is at least $17$.

Proof
We note that for $n = 239$ we have:

Thus the largest prime factor of $239^2 + 1$ is $13$.

Also see

 * Solution of Diophantine Equation $x^2 + 1 = 2 y^4$