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arXiv · 1409.3790

Rationality and power

Sam Chow·Bin Wei
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Abstract

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.

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Sam Chow, Bin Wei. 2014-09-12. Rationality and power. https://arxiv.org/abs/1409.3790

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