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TOT 271 1990 Autumn A J5 x_{n+1}=|x_n|-x_{n-1} has period 9

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June 8, 2024
algebraperiodicSequencerecurrence relation

Problem Statement

The numerical sequence {xn}\{x_n\} satisfies the condition xn+1=∣xn∣−xn−1x_{n+1}=|x_n|-x_{n-1} for all n>1n > 1. Prove that the sequence is periodic with period 99, i.e. for any n>1n > 1 we have xn=xn+9x_n = x_{n+9}.
(M Kontsevich, Moscow)
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