MathDB

2

Part of the 15th XMO

Problems(1)

Inequality in XMO

Source: XMO 15th

4/30/2024
nn is a integer and a1,a2,…,an∈[−1,1]a_1, a_2, \ldots, a_n\in[-1,1] are real numbers with ∑i=1nai=0 \sum_{i=1}^{n}a_{i}=0 ,try to find the maximum value of ∑1≤i,j≤n,i≠j∣ai−aj2∣ \sum_{1\leq i , j \leq n , i\ne j}|a_{i}-a^2_j|
inequalities