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Find real that there is no infinite sequence

Source: IMO Longlist 1989, Problem 90

September 18, 2008
inductionalgebra unsolvedalgebra

Problem Statement

Find the set of all a∈R a \in \mathbb{R} for which there is no infinite sequene (xn)n≥0⊂R (x_n)_{n \geq 0} \subset \mathbb{R} satisfying x_0 \equal{} a, and for n \equal{} 0,1, \ldots we have x_{n\plus{}1} \equal{} \frac{x_n \plus{} \alpha}{\beta x_n \plus{} 1} where αβ>0. \alpha \beta > 0.
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