IMO Shortlist 1998 problem N3
Dodao/la:
arhiva2. travnja 2012. Determine the smallest integer
![n\geq 4](/media/m/c/b/a/cbacc57c606ca84b7a7f6722e15ecaa8.png)
for which one can choose four different numbers
![a,b,c](/media/m/3/6/4/36454fdb50fc50f021324b33a6b513e3.png)
and
![d](/media/m/f/7/d/f7d3dcc684965febe6006946a72e0cd3.png)
from any
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
distinct integers such that
![a+b-c-d](/media/m/e/4/0/e401fb128678f75287c321ab09fd2c6b.png)
is divisible by
![20](/media/m/1/1/e/11e1c5de3460c5571469b3ff0f222b7e.png)
.
%V0
Determine the smallest integer $n\geq 4$ for which one can choose four different numbers $a,b,c$ and $d$ from any $n$ distinct integers such that $a+b-c-d$ is divisible by $20$.
Izvor: Međunarodna matematička olimpijada, shortlist 1998