IMO Shortlist 2007 problem A4


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April 2, 2012
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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
Source: Međunarodna matematička olimpijada, shortlist 2007