IMO Shortlist 2000 problem N5
Dodao/la:
arhiva2. travnja 2012. Prove that there exist infinitely many positive integers
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
such that
![p = nr,](/media/m/0/3/c/03c51368c0a5dc041dba9cb6ea3dcd4f.png)
where
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
and
![r](/media/m/3/d/f/3df7cc5bbfb7b3948b16db0d40571068.png)
are respectively the semiperimeter and the inradius of a triangle with integer side lengths.
%V0
Prove that there exist infinitely many positive integers $n$ such that $p = nr,$ where $p$ and $r$ are respectively the semiperimeter and the inradius of a triangle with integer side lengths.
Izvor: Međunarodna matematička olimpijada, shortlist 2000