### Abstract

The following conjecture of R. L. Graham is verified: If n≧n_{ 0}, where n_{ 0} is an explicitly computable constant, then for any n distinct positive integers a_{ 1}, a_{ 2}, ..., a_{ n} we have {Mathematical expression} a_{ i} /(a_{ i}, a_{ j} ) ≧ ≧n, and equality holds only in two trivial cases. Here (a_{ i}, a_{ j} ) stands for the greatest cnmmon divisor of a_{ i} and a_{ j} .

Original language | English (US) |
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Pages (from-to) | 67-71 |

Number of pages | 5 |

Journal | Combinatorica |

Volume | 6 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 1986 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Discrete Mathematics and Combinatorics