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\(x_1 = \sqrt[3]{3},\; x_{n+1}=(x_n)^{\sqrt[3]{3}}\). Find smallest \(n\) such that \(x_n\) is integer
02-20-2010, 02:52 PM
Post: #1
\(x_1 = \sqrt[3]{3},\; x_{n+1}=(x_n)^{\sqrt[3]{3}}\). Find smallest \(n\) such that \(x_n\) is integer
By indection, one can easily verify that
\[x_n = 3^{3^{-1+(n-1)/3}} \] thus \(n = 4\) is the answer.
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