IMO Shortlist 1998 problem N2
Dodao/la:
arhiva2. travnja 2012. Determine all pairs
![(a,b)](/media/m/e/2/6/e263229694cdbeb908488db2d0351f0a.png)
of real numbers such that
![a \lfloor bn \rfloor =b \lfloor an \rfloor](/media/m/d/9/d/d9d0a27900813a5216e1833bd1ad0886.png)
for all positive integers
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
. (Note that
![\lfloor x\rfloor](/media/m/f/7/3/f731119c18efc9ba5bad155f27328395.png)
denotes the greatest integer less than or equal to
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
.)
%V0
Determine all pairs $(a,b)$ of real numbers such that $a \lfloor bn \rfloor =b \lfloor an \rfloor$ for all positive integers $n$. (Note that $\lfloor x\rfloor$ denotes the greatest integer less than or equal to $x$.)
Izvor: Međunarodna matematička olimpijada, shortlist 1998