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a problem of ordered array from China TST

Source: 2017 China TST 4 Problem 3

March 22, 2017
combinatoricsset theoryQuadratic ResiduesChina TST

Problem Statement

Find the numbers of ordered array (x1,...,x100)(x_1,...,x_{100}) that satisfies the following conditions: (ii)x1,...,x100∈{1,2,..,2017}x_1,...,x_{100}\in\{1,2,..,2017\}; (iiii)2017∣x1+...+x1002017|x_1+...+x_{100}; (iiiiii)2017∣x12+...+x10022017|x_1^2+...+x_{100}^2.
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