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Sequence!

Source: notebook

November 22, 2005
calculusalgebra unsolvedalgebra

Problem Statement

The sequence x0,x1,x2,.....x_0,x_1,x_2,..... of real numbers is called with period pp,with pp being a natural number, when for each p≥2p\ge2, xn=xn+px_n=x_{n+p}. Prove that,for each p≥2p\ge2 there exists a sequence such that pp is its least period and xn+1=xn−1xnx_{n+1}=x_n-\frac{1}{x_n} (n=0,1,....)(n=0,1,....)
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