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x_{n+1}=y_n +1/x_n, y_{n+1}=z_n +1/y_n, z_{n+1}=x_n +1/z_n

Source: Austrian Polish 1981 APMC

April 30, 2020
recurrence relationSequenceunboundedalgebrabounded

Problem Statement

The sequences (xn),(yn),(zn)(x_n), (y_n), (z_n) are given by xn+1=yn+1xnx_{n+1}=y_n +\frac{1}{x_n},yn+1=zn+1yn y_{n+1}=z_n +\frac{1}{y_n},zn+1=xn+1znz_{n+1}=x_n +\frac{1}{z_n} for n≥0n \ge 0 where x0,y0,z0x_0,y_0, z_0 are given positive numbers. Prove that these sequences are unbounded.
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