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・ Hilbert's Nullstellensatz
・ Hilbert's paradox of the Grand Hotel
・ Hilbert's problems
・ Hilbert's program
・ Hilbert's second problem
・ Hilbert's seventeenth problem
・ Hilbert's seventh problem
・ Hilbert's sixteenth problem
・ Hilbert's sixth problem
・ Hilbert's syzygy theorem
・ Hilbert's tenth problem
・ Hilbert's theorem
・ Hilbert's theorem (differential geometry)
・ Hilbert's Theorem 90
・ Hilbert's third problem
Hilbert's thirteenth problem
・ Hilbert's twelfth problem
・ Hilbert's twentieth problem
・ Hilbert's twenty-first problem
・ Hilbert's twenty-fourth problem
・ Hilbert's twenty-second problem
・ Hilbert's twenty-third problem
・ Hilbert, West Virginia
・ Hilbert, Wisconsin
・ Hilbert–Bernays paradox
・ Hilbert–Bernays provability conditions
・ Hilbert–Burch theorem
・ Hilbert–Huang transform
・ Hilbert–Kunz function
・ Hilbert–Mumford criterion


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Hilbert's thirteenth problem : ウィキペディア英語版
Hilbert's thirteenth problem
Hilbert's thirteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by David Hilbert. It entails proving whether or not a solution exists for all 7th-degree equations using algebraic (variant: continuous) functions of two arguments. It was first presented in the context of nomography, and in particular "nomographic construction" — a process whereby a function of several variables is constructed using functions of two variables. Hilbert's conjecture, that it is not always possible to find such a solution, was disproven in 1957.
==Introduction==
Hilbert considered the seventh-degree equation
:x^7 + ax^3 + bx^2 + cx + 1 = 0
and asked whether its solution, ''x'', considered as a function of the three variables ''a'', ''b'' and ''c'', can be expressed as the composition of a finite number of two-variable functions.

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