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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 generalized taxicab number ： ウィキペディア英語版 generalized taxicab number In mathematics, the generalized taxicab number ''Taxicab''(''k'', ''j'', ''n'') is the smallest number which can be expressed as the sum of ''j'' ''k''th positive powers in ''n'' different ways. For ''k'' = 3 and ''j'' = 2, they coincide with taxicab numbers. :$\backslash mathrm(1,\; 2,\; 2)\; =\; 4\; =\; 1\; +\; 3\; =\; 2\; +\; 2.$ :$\backslash mathrm(2,\; 2,\; 2)\; =\; 50\; =\; 1^2\; +\; 7^2\; =\; 5^2\; +\; 5^2.$ :$\backslash mathrm(3,\; 2,\; 2)\; =\; 1729\; =\; 1^3\; +\; 12^3\; =\; 9^3\; +\; 10^3$ - famously stated by Ramanujan. Euler showed that :$\backslash mathrm(4,\; 2,\; 2)\; =\; 635318657\; =\; 59^4\; +\; 158^4\; =\; 133^4\; +\; 134^4.$ However, ''Taxicab''(5, 2, ''n'') is not known for any ''n'' ≥ 2; no positive integer is known which can be written as the sum of two fifth powers in more than one way.〔 〕 ==See also== *Cabtaxi number 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「generalized taxicab number」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.