Gelfond's theorem

If $a$ is an algebraic number different from $0$ or $1$, and $b$ irrational, then $a^b$ is transcendental (in particular irrational).

- A. O. Gelfond?,
*Transcendental and algebraic numbers*, Dover Publications, New York 1960, translation from 1st Russian edition by Leo F. Boron.

Created on January 14, 2011 at 15:16:31. See the history of this page for a list of all contributions to it.