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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Proizvolov's identity ： ウィキペディア英語版 Proizvolov's identity In mathematics, Proizvolov's identity is an identity concerning sums of differences of positive integers. The identity was posed by Vyacheslav Proizvolov as a problem in the 1985 All-Union Soviet Student Olympiads . To state the identity, take the first 2''N'' positive integers, :1, 2, 3, ..., 2''N'' − 1, 2''N'', and partition them into two subsets of ''N'' numbers each. Arrange one subset in increasing order: : Arrange the other subset in decreasing order: :$B\_1\; >\; B\_2\; >\; \backslash cdots\; >\; B\_N.$ Then the sum :$|A\_1-B\_1|\; +\; |A\_2-B\_2|\; +\; \backslash cdots\; +\; |A\_N-B\_N|$ is always equal to ''N''2. ==Example== Take for example ''N'' = 3. The set of numbers is then . Select three numbers of this set, say 2, 3 and 5. Then the sequences ''A'' and ''B'' are: :''A''1 = 2, ''A''2 = 3, and ''A''''3'' = 5; :''B''1 = 6, ''B''2 = 4, and ''B''''3'' = 1. The sum is :$|A\_1-B\_1|\; +\; |A\_2-B\_2|\; +\; |A\_3-B\_3|\; =\; |2-6|\; +\; |3-4|\; +\; |5-1|\; =\; 4+1+4\; =\; 9,$ which indeed equals 32. 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「Proizvolov's identity」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.