Problem

Source: Iran 3rd round 2013 - Algebra Exam - Problem 4

Tags: function, algebra, functional equation



Find all functions $f:\mathbb{R}\rightarrow \mathbb{R}$ such that $f(0) \in \mathbb Q$ and \[f(x+f(y)^2 ) = {f(x+y)}^2.\] (25 points)