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Thue-Siegel-Roth theorem : ウィキペディア英語版 | Thue–Siegel–Roth theorem
In mathematics, the Thue–Siegel–Roth theorem, also known simply as Roth's theorem, is a fundamental result in diophantine approximation to algebraic numbers. It is of a qualitative type, stating that a given algebraic number may not have too many rational number approximations, that are 'very good'. Over half a century, the meaning of ''very good'' here was refined by a number of mathematicians, starting with Joseph Liouville in 1844 and continuing with work of , , , and . == Statement ==
The Thue–Siegel–Roth theorem states that any irrational algebraic number has approximation exponent equal to 2, ''i.e.'', for given , the inequality : with a positive number depending only on and .
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