For a positive integer \( n \), find all continuous functions \( f: \mathbb{R} \to \mathbb{R} \) such that
\[
\sum_{k=0}^n \binom{n}{k} f(x^{2^k}) = 0
\]
for all \( x \in \mathbb{R} \).

The best solution was submitted by Kawano Ren (Kaisei Senior High School, +4). Congratulations!

Here is the best solution of problem 2022-16.

Other solutions were submitted by 김찬우 (연세대학교 수학과, +3), 기영인 (KAIST 22학번, +3), 여인영 (KAIST 물리학과 20학번, +3). Late solutions were not graded.