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, 2015

Number theory Difficulty 6.0 National Olympiad Prove it Hungary

For every positive integer $n$ , let $P(n)$ be the greatest prime divisor of $n^2+1$ . Show that there are infinitely many quadruples $(a,b,c,d)$ of positive integers that satisfy $a<b<c<d$ and $P(a)=P(b)=P(c)=P(d)$ .
(5 pont)

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