Hurwitz's theorem (number theory)
In number theory, Hurwitz's theorem, named after Adolf Hurwitz, gives a bound on a Diophantine approximation. The theorem states that for every irrational number ξ there are infinitely many relatively prime integers m, n such that The condition that ξ is irrational cannot be omitted. Moreover the constant is the best possible; if we replace by any number and we let (the golden ratio) then there exist only finitely many relatively prime integers m, n such that the formula above holds. The theorem is equivalent to the claim that the Markov constant of every number is larger than .
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Hurwitz's theorem (number theory)
In number theory, Hurwitz's theorem, named after Adolf Hurwitz, gives a bound on a Diophantine approximation. The theorem states that for every irrational number ξ there are infinitely many relatively prime integers m, n such that The condition that ξ is irrational cannot be omitted. Moreover the constant is the best possible; if we replace by any number and we let (the golden ratio) then there exist only finitely many relatively prime integers m, n such that the formula above holds. The theorem is equivalent to the claim that the Markov constant of every number is larger than .
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Die Mathematik kennt eine Anza ...... die Güte der Approximation an.
@de
En teoría de números, el teore ...... a fórmula de arriba se cumpla.
@es
En théorie des nombres, le thé ...... inité de rationnels tels que .
@fr
In number theory, Hurwitz's th ...... every number is larger than .
@en
In teoria dei numeri, il teore ...... r i quali la formula è valida.
@it
Na teoria dos números, teorema ...... do que a fórmula acima mantém.
@pt
Στη Θεωρία των Αριθμών, το Θεώ ...... τε να ισχύει ο τύπος παραπάνω.
@el
Теорема Гурвица — результат те ...... иональных чисел рациональными.
@ru
Теорема Гурвіца — результат те ...... Адольфом Гурвіцем у 1891 році.
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数論において，フルヴィッツの定理（英: Hurwitz's ...... 立つような互いに素な整数 m, n は有限個しか存在しない．
@ja
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Die Mathematik kennt eine Anza ...... die Güte der Approximation an.
@de
En teoría de números, el teore ...... a fórmula de arriba se cumpla.
@es
En théorie des nombres, le thé ...... inité de rationnels tels que .
@fr
In number theory, Hurwitz's th ...... every number is larger than .
@en
In teoria dei numeri, il teore ...... r i quali la formula è valida.
@it
Na teoria dos números, teorema ...... do que a fórmula acima mantém.
@pt
Στη Θεωρία των Αριθμών, το Θεώ ...... τε να ισχύει ο τύπος παραπάνω.
@el
Теорема Гурвица — результат те ...... иональных чисел рациональными.
@ru
Теорема Гурвіца — результат те ...... Адольфом Гурвіцем у 1891 році.
@uk
数論において，フルヴィッツの定理（英: Hurwitz's ...... 立つような互いに素な整数 m, n は有限個しか存在しない．
@ja
label
Hurwitz's theorem (number theory)
@en
Satz von Hurwitz (Zahlentheorie)
@de
Teorema de Hurwitz (teoria dos números)
@pt
Teorema de Hurwitz (teoría de números)
@es
Teorema di Hurwitz (teoria dei numeri)
@it
Théorème de Hurwitz (approximation diophantienne)
@fr
Θεώρημα του Χούρβιτς
@el
Теорема Гурвица (теория чисел)
@ru
Теорема Гурвіца (теорія чисел)
@uk
フルヴィッツの定理 (数論)
@ja