An extension of Nathanson’s Theorem on representation functions

Abstract

For a given integer n and a set S ⊆ N denote by R h,S (1) the number of solutions of the equation \(n = {s_{{i_1}}} + ... + {s_{{i_h}}},{s_{{i_j}}} \in S,j = 1,...,h\). In this paper we determine all pairs (A;B), A,B ⊆ N for which R h,A (1)(n) = R h,B (1)(n) from a certain point on, where h is a power of a prime. We also discuss the composite case.

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Correspondence to Eszter Rozgonyi.

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This author was supported by the OTKA Grant No. K109789.

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Rozgonyi, E., Sándor, C. An extension of Nathanson’s Theorem on representation functions. Combinatorica 37, 521–537 (2017). https://doi.org/10.1007/s00493-015-3311-8

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Mathematics Subject Classification (2000)

  • 11B34