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The Erdös-Fuchs theorem on the square of a power series

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Publication Date
Volume
9
Issue
3
Identifiers
DOI: 10.1016/0022-314x(77)90068-3

Abstract

Abstract Erdös and Fuchs proved that if a 1, a 2,… is a sequence of nonnegative integers and R( n) is the number of ordered pairs ( i, j) with a i + a j ≤ n, then it is impossible to have R(n) = An + o(n 1 4 log −1 2 n) as n → + ∞, for some positive constant A. This paper gives a generalization of this result, in which An is replaced by a function of n whose second differences are nonnegative from some point on.

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