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In mathematics, a Kaprekar number for a given base is a non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again. For instance, 45 is a Kaprekar number, because 45² = 2025 and 20+25 = 45. The Kaprekar numbers are named after D. R. Kaprekar. == Definition == Let ''X'' be a non-negative integer. ''X'' is a Kaprekar number for base ''b'' if there exist non-negative integers ''n'', ''A'', and positive number ''B'' satisfying: : ''X''² = ''Abn'' + ''B'', where 0 < ''B'' < ''bn'' : ''X'' = ''A'' + ''B'' Note that ''X'' is also a Kaprekar number for base ''bn'', for this specific choice of ''n''. More narrowly, we can define the set ''K(N)'' for a given integer ''N'' as the set of integers ''X'' for which〔Ianucci (2000)〕 : ''X''² = ''AN'' + ''B'', where 0 < ''B'' < ''N'' : ''X'' = ''A'' + ''B'' Each Kaprekar number ''X'' for base ''b'' is then counted in one of the sets ''K(b)'', ''K(b²)'', ''K(b³)'',…. 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「Kaprekar number」の詳細全文を読む スポンサード リンク
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