### Abstract

Let A be a set of nonnegative integers such that d_{L}(A) = w > 0. Let k be the least integer satisfying k ≥ 1 w. It is proved that there is an infinite arithmetic progression with difference at most k + 1 such that every term of the progression can be written as a sum of exactly k^{2} - k distinct terms of A, and there is an infinite arithmetic progression with difference at most k^{2} - k such that every term of the progression can be written as a sum of exactly k + 1 distinct terms of A. A solution is also obtained to the infinite analog of a problem of Erdös and Freud on powers of 2 and on square-free numbers that can be represented as bounded sums of distinct elements chosen from a set A with positive density.

Original language | English |
---|---|

Pages (from-to) | 159-166 |

Number of pages | 8 |

Journal | Journal of Number Theory |

Volume | 28 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 1988 |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Number Theory*,

*28*(2), 159-166. https://doi.org/10.1016/0022-314X(88)90063-7