IMO Shortlist 2007 problem A4
Dodao/la:
arhiva2. travnja 2012. Find all functions
satisfying
for all pairs of positive reals
and
. Here,
denotes the set of all positive reals.
Proposed by Paisan Nakmahachalasint, Thailand
%V0
Find all functions $f: \mathbb{R}^{ + }\to\mathbb{R}^{ + }$ satisfying $f\left(x + f\left(y\right)\right) = f\left(x + y\right) + f\left(y\right)$ for all pairs of positive reals $x$ and $y$. Here, $\mathbb{R}^{ + }$ denotes the set of all positive reals.
Proposed by Paisan Nakmahachalasint, Thailand
Izvor: Međunarodna matematička olimpijada, shortlist 2007