nLab Gelfond's theorem

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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.

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