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In mathematics, in the area of combinatorial number theory, the Erdős–Fuchs theorem is a statement about the number of ways that numbers can be represented as a sum of two elements of a given set, stating that the average order of this number cannot be close to being a linear function. The theorem is named after Paul Erdős and Wolfgang Heinrich Johannes Fuchs. ==Statement== Let ''A'' be a subset of the natural numbers and ''r''(''n'') denote the number of ways that a natural number ''n'' can be expressed as the sum of two elements of ''A'' (taking order into account). We consider the average : The theorem states that : cannot hold unless ''C'' = 0. 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「Erdős–Fuchs theorem」の詳細全文を読む スポンサード リンク
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