翻訳と辞書 Words near each other ・ Divis transmitting station ・ Divisa ・ Divisa Alegre ・ Divisa Nova ・ Divisaderan ・ Divisadero ・ Divisadero (novel) ・ Divisaderos ・ Divisaderos Municipality ・ Diviseema ・ Divisi ・ Divisia index ・ Divisia monetary aggregates index ・ Divisibility (ring theory) ・ Divisibility rule ・ Divisibility sequence ・ Divisible group ・ Divisible profit ・ Division ・ Division (10 Years album) ・ Division (botany) ・ Division (business) ・ Division (country subdivision) ・ Division (CTA North Side Main Line station) ・ Division (CTA station) ・ Division (horticulture) ・ Division (mathematics) ・ Division (military) ・ Division (music) ・ Division (naval) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Divisibility sequence ： ウィキペディア英語版 Divisibility sequence In mathematics, a divisibility sequence is an integer sequence $\_$ such that for all natural numbers ''m'', ''n'', :$\backslash textm\backslash mid\; n\backslash texta\_m\backslash mid\; a\_n,$ i.e., whenever one index is a multiple of another one, then the corresponding term also is a multiple of the other term. The concept can be generalized to sequences with values in any ring where the concept of divisibility is defined. A strong divisibility sequence is an integer sequence $\_$ such that for all natural numbers ''m'', ''n'', :$\backslash gcd(a\_m,a\_n)\; =\; a\_.$ Note that a strong divisibility sequence is immediately a divisibility sequence; if $m\backslash mid\; n$, immediately $gcd(m,n)\; =\; m$. Then by the strong divisibility property, $gcd(a\_m,a\_n)\; =\; a\_m$ and therefore $a\_m\backslash mid\; a\_n$. ==Examples== * Any constant sequence is a strong divisibility sequence. * Every sequence of the form $a\_n\; =\; kn$, for some nonzero integer ''k'', is a divisibility sequence. * Every sequence of the form $a\_n\; =\; A^n\; -\; B^n$ for integers $A>B>0$ is a divisibility sequence. * The Fibonacci numbers ''F'' = (1, 1, 2, 3, 5, 8,...) form a strong divisibility sequence. * More generally, Lucas sequences of the first kind are divisibility sequences. * Elliptic divisibility sequences are another class of such sequences. 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「Divisibility sequence」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.