Balkan Math Olympiad 2000 - Problem 1: A classic functional equation

Latex:
Find all functions $f: \mathbb R \to \mathbb R$ such that\[ f( xf(x) + f(y) ) = f^2(x) + y \]for all $x,y\in \mathbb R$.

[Oppenheimer-mrpk]

I love the chill vibe of your videos sir! It's like you're experimenting and solving it from our perspective, you're my favourite youtuber!

[batapanos]

Love your videos! Am a math olympiad candidate and your channel has helped a lot.. I'd also like to see problem 4 of 2012 JBMO cause i can't find a solution online to check whether mine is fully correct

[ujjwalkesari]

Great Video👍
Please try to make some more basic functional equations as well

[joelgerlach]

Oh lol Evan Chen had this problem as an application problem for OTIS. I wonder how often people forget about the pointwise trap.