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(f(n+1) -1)^2 +(f (n)-1)^2 = 2f(n) f(n+1) + 4 (Chile NMO 1989 P6)

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November 19, 2021
algebrafunctionfunctional equationfunctional

Problem Statement

The function ff, with domain on the set of non-negative integers, is defined by the following : ∙\bullet f(0)=2f (0) = 2 ∙\bullet (f(n+1)−1)2+(f(n)−1)2=2f(n)f(n+1)+4(f (n + 1) -1)^2 + (f (n)-1) ^2 = 2f (n) f (n + 1) + 4, taking f(n)f (n) the largest possible value. Determine f(n)f (n).
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