### Abstract

In this paper we discuss the following conjecture: Conjecture: Let D = (D_{1}, … , D_{n}), D ⊂ N, N the set of positive integers. Then there exists a permutation of N, call it (a_{k}: k ϵ N) such that (|αf_{k+1} − a_{k}| : k ϵ N) = D iff (D_{1}, …, D_{n}) = l. We also consider the following question: Question: For what sets D = (D_{1}, ‖, D_{n}) does there exist an integer M ϵ N and a permutation (|b_{k:+1}: k = 1,… , M) of (1, …, M) such that (|b_{k+1} − b_{k}|: k = 1, …, M - l) = D. We answer the conjecture and the following question in the affirmative if the set D has the following property: For each D_{r}Espilon; D there is a D_{s}ϵ D such that (D_{r}, D_{s}) = 1.

Original language | English (US) |
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Pages (from-to) | 527-531 |

Number of pages | 5 |

Journal | Pacific Journal of Mathematics |

Volume | 82 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1979 |

### ASJC Scopus subject areas

- Mathematics(all)