Rationality and power

By Sam Chow, Bin Wei. 2014

126 citations recorded by the source corpus.

We produce an infinite family of transcendental numbers which, when raised to their own power, become rational. We extend the method, to investigate positive rational solutions to the equation $x^x = \alpha$, where $\alpha$ is a fixed algebraic number. We then explore the consequences of $x^{P(x)}$ being rational, if $x$ is rational and $P(x)$ is a fixed integer polynomial.

Subfields: Geometry and Topology, Mathematical Physics, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/ff8e1d68a8058572a0d4c61f6e29c2987b959358

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Citations in the corpus

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