NAGEL PROBLEMS(NUMBER THEORY)

Problem:given positive integer c,prove that there exist infitive positive integer n such that largest prime divisor of $n^2+1$ is greater than $cn$
Link:1,https://artofproblemsolving.com/community/c6h126781
         :2,http://artofproblemsolving.com/community/c6h215221p5291883

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