Using Schmidt's Subspace Theorem, this paper improves and extends an existing transcendence result for sequences of algebraic numbers. The theorems thus produced correspond to a central theorem on the irrationality of sequences due to Erd\H{o}s.
Notes on the Theory of Algebraic Numbers
Rational approximations to $\sqrt[3]{2}$ and other algebraic numbers revisited
On periodic sequences for algebraic numbers
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