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Found problems: 1

2024 USAJMO, 5
Tags: functional equation , function , pointwise trap
Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ that satisfy \[ f(x^2-y)+2yf(x)=f(f(x))+f(y) \] for all $x,y\in\mathbb{R}$. [i]Proposed by Carl Schildkraut[/i]