|
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 hypothesis 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. == References == * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Hurwitz's theorem (number theory)」の詳細全文を読む スポンサード リンク
|