Mathematical and Physical Journal
for High Schools
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# Problem A. 643. (April 2015)

A. 643. For every positive integer $\displaystyle n$, let $\displaystyle P(n)$ be the greatest prime divisor of $\displaystyle n^2+1$. Show that there are infinitely many quadruples $\displaystyle (a,b,c,d)$ of positive integers that satisfy $\displaystyle a<b<c<d$ and $\displaystyle P(a)=P(b)=P(c)=P(d)$.

(5 pont)

Deadline expired on May 11, 2015.

### Statistics:

 2 students sent a solution. 5 points: Janzer Barnabás, Williams Kada.

Problems in Mathematics of KöMaL, April 2015