Hilbert's seventh problem asks:
- Is ab transcendental, for algebraic a ≠ 0,1 and irrational algebraic b?
This problem was solved by Aleksandr Gelfond in 1934, and refined by Theodor Schneider (1911 - ) in 1935. They proved that ab is transcendental where b is both algebraic and irrational. This result is known as Gelfond's theorem or the Gelfond-Schneider theorem.
From the point of view of generalisations, this is the case
- blog (α) + log(β) = 0
See also:
- Alan Baker
- Gelfond's conjecture
- Hilbert's problems