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Gelfond's theorem

Gelfond's theorem, also known as the Gelfond-Schneider theorem, asserts that ab is a transcendental number if (1) a is an algebraic number and not equal to either 0 or 1, and (2) b is algebraic and also an irrational number. Gelfond's theorem enables the seventh of David Hilbert's famous problems to be solved.

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