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x_{n+1} = a / ( 1+x(n)^2)

Source: Vietnam TST 1996 for the 37th IMO, problem 6

June 26, 2005

algebra unsolvedalgebra

Problem Statement

Find all reals

a

such that the sequence

\{x(n)\}

n=0,1,2, \ldots

that satisfy:

x(0)=1996

and

x_{n+1} = \frac{a}{1+x(n)^2}

for any natural number

n

has a limit as n goes to infinity.