MathDB
2002 KJMO P6

Source: 2002 KJMO

June 29, 2024
algebrasolutions

Problem Statement

For given positive integer aa, find every (x1,x2,…,x2002)(x_1, x_2, …, x_{2002}) that satisfies the following:
(1) x1≥x2≥…≥x2002≥0x_1 \geq x_2 \geq … \geq x_{2002} \geq 0
(2) 0<x1+x2+…+x2003<a+10< x_1+x_2+…+x_{2003}<a+1
(3) x12+x22+…+x20032+9=a2 x^2_1+x^2_2+…+x^2_{2003}+9=a^2
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