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System with 2024 variables, but how many are equal?

Source: Francophone 2024, Junior P1

April 4, 2024
algebra proposedsystem of equationsalgebra

Problem Statement

Find the largest integer kk with the following property: Whenever real numbers x1,x2,…,x2024x_1,x_2,\dots,x_{2024} satisfy x12=(x1+x2)2=⋯=(x1+x2+⋯+x2024)2,x_1^2=(x_1+x_2)^2=\dots=(x_1+x_2+\dots+x_{2024})^2, at least kk of them are equal.
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