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・ Hilbert's nineteenth problem
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Hilbert's seventh problem
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Hilbert's seventh problem : ウィキペディア英語版
Hilbert's seventh problem
Hilbert's seventh problem is one of David Hilbert's list of open mathematical problems posed in 1900. It concerns the irrationality and transcendence of certain numbers (''Irrationalität und Transzendenz bestimmter Zahlen'').
==Statement of the problem==
Two specific questions are asked:
#In an isosceles triangle, if the ratio of the base angle to the angle at the vertex is algebraic but not rational, is then the ratio between base and side always transcendental?
#Is a^b always transcendental, for algebraic a \not\in \ and irrational algebraic b?

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