### Abstract

We study the sumset A + k · A for the first non trivial case, k = 3, where k · A = {k · a, a ∈ A}. We prove that |A+ 3 · A| ≥ 4|A|- 4 and that the equality holds only for A = {0, 1, 3}, A = {0, 1, 4}, A = 3 · {0,. . ., n} [ (3 · {0,. . ., n} + 1) and all the affine transforms of these sets.

Original language | English |
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Title of host publication | A sumset problem |

Pages | 85-96 |

Number of pages | 12 |

Volume | 2 |

Edition | 1 |

Publication status | Published - 1 Jan 2012 |

### Publication series

Name | Journal of Combinatorics and Number Theory |
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## Cite this

Cilleruelo, J., Silva, M. A., & Vinuesa, C. (2012). A sumset problem. In

*A sumset problem*(1 ed., Vol. 2, pp. 85-96). (Journal of Combinatorics and Number Theory).