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Benelux Mathematical Olympiad 2016, Problem 1

Source:

May 1, 2016
number theory

Problem Statement

Find the greatest positive integer NN with the following property: there exist integers x1,...,xNx_1, . . . , x_N such that xi2−xixjx^2_i - x_ix_j is not divisible by 11111111 for any i≠j.i\ne j.
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