Question 1
Let $P(x)$ be a nonconstant monic polynomial with real coefficients. Find every continuous function $f:\mathbb R\to\mathbb R$ such that
$$f\bigl(f(P(x))+y+2023f(y)\bigr)=P(x)+2024f(y)$$
for all $x,y\in\mathbb R$.
Annual practice duration is 540 minutes, combining the two source-stated 270-minute exam days. The source gives no point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.
$$f\bigl(f(P(x))+y+2023f(y)\bigr)=P(x)+2024f(y)$$
for all $x,y\in\mathbb R$.
Annual practice duration is 540 minutes, combining the two source-stated 270-minute exam days. The source gives no point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.