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It is true that an irrational number to the power of an irrational number could be rational. I am curious about the following:

Are there conditions that imply irrational to the power of irrational will be rational ?

Möbius Trip
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  • The pointer to the duplicate is mistaken. The first sentence is NOT a question, but is instead declarative (asserting the truth of the answers to the linked question!) The second sentence is a question that could actually use answering. – John Hughes Oct 04 '16 at 14:09

1 Answers1

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We can find a class of examples using the fact that, for $k$ integer, $\ln k$ is irrational (as a consequence of Gelfond-Schneider theorem) and $e^{\ln k}=k$ is rational.

Emilio Novati
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