IMO Shortlist 2007 problem A4
Dodao/la:
arhiva2. travnja 2012. Find all functions
![f: \mathbb{R}^{ + }\to\mathbb{R}^{ + }](/media/m/a/7/e/a7e0bf6391e12544c3521e66761f70a5.png)
satisfying
![f\left(x + f\left(y\right)\right) = f\left(x + y\right) + f\left(y\right)](/media/m/4/0/e/40efbb65eeeea72ecb7a7d9d50d5acc8.png)
for all pairs of positive reals
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
and
![y](/media/m/c/c/0/cc082a07a517ebbe9b72fd580832a939.png)
. Here,
![\mathbb{R}^{ + }](/media/m/7/6/b/76b8ab740ef96cf7e5e0e929663a2103.png)
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