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.


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

Problems in Mathematics of KöMaL, April 2015