IMO Shortlist 1967 problem 2
Dodao/la:
arhiva2. travnja 2012. Let
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
and
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
be positive integers such that
![1 \leq n \leq N+1](/media/m/7/3/a/73ab1ebbec4f4a5c92935c08334d61a7.png)
,
![1 \leq k \leq N+1](/media/m/a/6/9/a69a200fdc4310e7905369b1666c3ea3.png)
. Show that:
%V0
Let $n$ and $k$ be positive integers such that $1 \leq n \leq N+1$, $1 \leq k \leq N+1$. Show that: $$\min_{n \neq k} |\sin n - \sin k| < \frac{2}{N}.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1967