Consider any sequence \( a_1,\dots, a_n \) of non-negative integers in \(\{0,1,\dots, m\}\). Prove that \[|\{ a_i+ a_j + (j-i): 1\leq i < j \leq n \}|\geq m \] when \(m= \lfloor \frac{1}{4} n^{2/3} \rfloor \).

The best solution was submitted by 김준홍 (수리과학과 석박통합과정, +4). Congratulations!

Here is the best solution of problem 2025-03.

Another solution was submitted by Anar Rzayev (수리과학과 19학번, +2).