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TOT 551 1997 Autumn J A1 x_{n+2} =x_n - 1/x_{n+1}

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September 11, 2024
algebraSequencerecurrence relation

Problem Statement

The sequence x1,x2,...x_1,x_2, ... is defined by the following equations: x1=19,  x2=97,  xn+2=xn−1xn+1x_1=19, \ \ x_2=97, \ \ x_{n+2} =x_n - \frac{1}{x_{n+1}} for n≥1n \ge 1. Prove that there exists a positive integer kk such that xk=0x_k=0 and find kk.
(A Berzinsh)
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