### Abstract

Let a_{1} <a_{2} <… be an infinite sequence of positive integers and denote by R(n) the number of solutions of n = a_{i} + a_{j}. The authors prove that if F(n) is a monotonic increasing arithmetic function with F(n) → +∞ and F(n) = o(n(log n)^{-2}) then |R(n) - F(n)| = o((F(n))^{1/2}) cannot hold.

Original language | English |
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Pages (from-to) | 347-357 |

Number of pages | 11 |

Journal | Pacific Journal of Mathematics |

Volume | 118 |

Issue number | 2 |

Publication status | Published - 1985 |

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### ASJC Scopus subject areas

- Mathematics(all)