For given \(a, b \in \mathbb{R}\) and \(c \in \mathbb{Z}\), find all function \(f: \mathbb{R} \to \mathbb{R}\) which is continuous at 0 and satisfies
\[
f(ax) = f(bx) + x^c \quad \forall x\in \mathbb{R}\setminus \{0\}.
\]
The best solution was submitted by 정서윤 (수리과학과 학사과정, +4). Congratulations!
Here is the best solution of problem 2025-09.
Other solutions were submitted by 김동훈 (수리과학과 22학번, +3), 신민규 (수리과학과 24학번, +3), 채지석 (수리과학과 석박통합과정, +3), Anar Rzayev (수리과학과 19학번, +2), 김준홍 (수리과학과 석박통합과정, +2), 이명규 (전기및전자공학부 20학번, +2).
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