### Abstract

According to Nathanson, an n-dimensional N-set is a compact subset A of ℝn such that for every x ε ℝ^{n} there is y ε A with y - x ε ℤ^{n}. We prove that every two dimensional N-set A must contain distinct points x, y such that x - y is in ℤ^{2} and x - y is neither horizontal nor vertical. This answers a question of P. Hegarty and M. Nathanson.

Original language | English (US) |
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Pages (from-to) | 2431-2434 |

Number of pages | 4 |

Journal | Proceedings of the American Mathematical Society |

Volume | 139 |

Issue number | 7 |

DOIs | |

State | Published - Jul 1 2011 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

Borisov, L., & Jin, R. (2011). Finding integral diagonal pairs in a two dimensional N-set.

*Proceedings of the American Mathematical Society*,*139*(7), 2431-2434. https://doi.org/10.1090/S0002-9939-2010-10688-3