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Turkey NMO 2001 Problem 2

Source: Turkey NMO 2001 Problem 2

September 30, 2011
algebra unsolvedalgebra

Problem Statement

(xn)−∞<n<∞(x_{n})_{-\infty<n<\infty} is a sequence of real numbers which satisfies xn+1=xn2+107x_{n+1}=\frac{x_{n}^2+10}{7} for every n∈Zn \in \mathbb{Z}. If there exist a real upperbound for this sequence, find all the values x0x_{0} can take.
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