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Prove that IMO Longlist 1989 is periodic

Source: IMO Longlist 1989, Problem 15

September 18, 2008
functionalgebrarational functionalgebra unsolved

Problem Statement

A sequence a1,a2,a3,… a_1, a_2, a_3, \ldots is defined recursively by a_1 \equal{} 1 and a_{2^k\plus{}j} \equal{} \minus{}a_j (j \equal{} 1, 2, \ldots, 2^k). Prove that this sequence is not periodic.
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