For each $i \in \mathbb{N}$, let $F_i$ be the $i$-th Fibonacci number where $F_0=0, F_1=1$ and $F_{i+1}=F_{i}+F_{i-1}$ for each $i\geq 1$.
For $n>m$, we divide $F_n$ by $F_m$ to obtain the remainder $R$. Prove that either $R$ or $F_m-R$ is a Fibonacci number.

The best solution was submitted by 고성훈 (수리과학과 2018학번, +4). Congratulations!

Here is his solution of problem 2020-24.

Other solutions was submitted by Abdirakhman Ismail (2020학번), 이준호 (수리과학과 2016학번, +3).