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・ Erdős arcsine law
・ Erdős cardinal
・ Erdős conjecture on arithmetic progressions
・ Erdős distinct distances problem
・ Erdős number
・ Erdős Prize
・ Erdős space
・ Erdősmecske
・ Erdősmárok
・ Erdős–Anning theorem
・ Erdős–Bacon number
・ Erdős–Borwein constant
・ Erdős–Burr conjecture
・ Erdős–Diophantine graph
・ Erdős–Faber–Lovász conjecture
Erdős–Fuchs theorem
・ Erdős–Gallai theorem
・ Erdős–Graham problem
・ Erdős–Gyárfás conjecture
・ Erdős–Hajnal conjecture
・ Erdős–Kac theorem
・ Erdős–Ko–Rado theorem
・ Erdős–Mordell inequality
・ Erdős–Nagy theorem
・ Erdős–Nicolas number
・ Erdős–Pósa theorem
・ Erdős–Rado theorem
・ Erdős–Rényi model
・ Erdős–Stone theorem
・ Erdős–Straus conjecture


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Erdős–Fuchs theorem : ウィキペディア英語版
Erdős–Fuchs theorem
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
:R(n) = \frac.
The theorem states that
:R(n) = C + O\left(n^\right)
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)
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