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Module expression

Source: RMO District Round, Bucharest 2008, Grade 10, Problem 1

January 27, 2008
abstract algebraalgebra proposedalgebra

Problem Statement

Let z∈C z \in \mathbb{C} such that for all k∈1,3‾ k \in \overline{1, 3}, |z^k \plus{} 1| \le 1. Prove that z \equal{} 0.
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