IMO Shortlist 2010 problem A1


Kvaliteta:
  Avg: 5,0
Težina:
  Avg: 6,0
Dodao/la: arhiva
23. lipnja 2013.
LaTeX PDF
Find all function f:\mathbb{R}\rightarrow\mathbb{R} such that for all x,y\in\mathbb{R} the following equality holds f(\left\lfloor x\right\rfloor y)=f(x)\left\lfloor f(y)\right\rfloor


where \left\lfloor a\right\rfloor is greatest integer not greater than a.

Proposed by Pierre Bornsztein, France
Izvor: Međunarodna matematička olimpijada, shortlist 2010