Question 1
Let $\alpha$ be real and define $\varphi(x)=x^2e^{\alpha x}$ for $x\in\mathbb R$. Find all functions $f:\mathbb R\to\mathbb R$ satisfying, for every $x,y\in\mathbb R$, $$f(\varphi(x)+f(y))=y+\varphi(f(x)).$$
The source gives no point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.
The source gives no point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.