Year: 2014
Type: preprint
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 $x^x = α$, where $α$ 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.
Source: arXiv (Cornell University)
Authors: Chow, Sam, Wei, Bin
Institution: Shandong University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2239326690