The first approach to a solution for Hilbert's 7th problem, for 10 points, identify this theorem which states that if a is algebraic and b is both algebraic and irrational, then a raised to the bth power is transcendental, which is sometimes also named for its independent discoverer Theodor ?
Zuehlke showed that Wiles' proof of Fermat's last theorem can be extended to Gaussian integers using this statement, and comically noted that the proof "almost fits in the margin." Its namesake and Kuzmin used Siegel's lemma to extend it to the real quadratic field, and it was generalized by Alan Baker, who proved the linear independence of an arbitrary number of logarithms. Proving Schanuel's conjecture would imply both the Lindemann-Weierstrass theorem and this theorem. Its namesake also lends his name to a constant sometimes called Hilbert's constant, which is equal to 2 raised to the square root of 2. The first approach to a solution for Hilbert's 7th problem, for 10 points, identify this theorem which states that if a is algebraic and b is both algebraic and irrational, then a raised to the bth power is transcendental, which is sometimes also named for its independent discoverer Theodor ? Schneider.
Zuehlke showed that Wiles' proof of Fermat's last theorem can be extended to Gaussian integers using this statement, and comically noted that the proof "almost fits in the margin."
{Gelfond's} theorem [accept {Gelfond}-{Schneider theorem} before "{Schneider}"]