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(271) 5

Part of 1990 Tournament Of Towns

Problems(1)

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

Source:

6/8/2024
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)
algebraperiodicSequencerecurrence relation