IMO Shortlist 2003 problem N5
Dodao/la:
arhiva2. travnja 2012. An integer
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
is said to be good if
![|n|](/media/m/b/7/6/b76fd9ea3de8598f12e23a222d7221cc.png)
is not the square of an integer. Determine all integers
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
with the following property:
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
can be represented, in infinitely many ways, as a sum of three distinct good integers whose product is the square of an odd integer.
%V0
An integer $n$ is said to be good if $|n|$ is not the square of an integer. Determine all integers $m$ with the following property: $m$ can be represented, in infinitely many ways, as a sum of three distinct good integers whose product is the square of an odd integer.
Izvor: Međunarodna matematička olimpijada, shortlist 2003