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In mathematics, the Prouhet–Tarry–Escott problem asks for two disjoint sets ''A'' and ''B'' of ''n'' integers each, such that: : for each integer ''i'' from 1 to a given ''k''. This problem was named after Eugène Prouhet, who studied it in the early 1850s, and Gaston Tarry and Escott, who studied it in the early 1910s. The problem originates from letters of Christian Goldbach and Leonhard Euler (1750/1751). == Examples == It has been shown that ''n'' must be strictly greater than ''k''. The largest value of ''k'' for which a solution with ''n'' = ''k''+1 is known is given by ''A'' = , ''B'' = for which ''k'' = 11.〔(Solution found by Nuutti Kuosa, Jean-Charles Meyrignac and Chen Shuwen, in 1999 ).〕 An example for ''n'' = 6 and ''k'' = 5 is given by the two sets and , because: : 01 + 51 + 61 + 161 + 171 + 221 = 11 + 21 + 101 + 121 + 201 + 211 : 02 + 52 + 62 + 162 + 172 + 222 = 12 + 22 + 102 + 122 + 202 + 212 : 03 + 53 + 63 + 163 + 173 + 223 = 13 + 23 + 103 + 123 + 203 + 213 : 04 + 54 + 64 + 164 + 174 + 224 = 14 + 24 + 104 + 124 + 204 + 214 : 05 + 55 + 65 + 165 + 175 + 225 = 15 + 25 + 105 + 125 + 205 + 215. 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「Prouhet–Tarry–Escott problem」の詳細全文を読む スポンサード リンク
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