\(x_1 = \sqrt[3]{3},\; x_{n+1}=(x_n)^{\sqrt[3]{3}}\). Find smallest \(n\) such that \(x_n\) is integer

02202010, 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
\[x_n = 3^{3^{1+(n1)/3}} \] thus \(n = 4\) is the answer. 

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