IMO Shortlist 2005 problem A2


Kvaliteta:
  Avg: 2,8
Težina:
  Avg: 6,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
We denote by \mathbb{R}^+ the set of all positive real numbers.

Find all functions f: \mathbb R^ + \rightarrow\mathbb R^ + which have the property: f\left(x\right)f\left(y\right) = 2f\left(x + yf\left(x\right)\right) for all positive real numbers x and y.
Izvor: Međunarodna matematička olimpijada, shortlist 2005