## Abstract

Let n be a positive integer. The factor-difference set D(n) of n is the set of absolute values d of the differences between the factors of any factorization of n as a product of two integers. Erdos and Rosenfeld [The factor-difference set of integers, Acta Arith. 79(4) (1997) 353-359] ask whether for every positive integer n there exist integers N1 < ⋯ < Nn such that | 1nD(N i)|≥ n, and prove this is true when n = 2. Urroz [A note on a conjecture of Erdos and Rosenfeld, J. Number Theory 78(1) (1999) 140-143] shows the result true for n = 3. The ideas of this paper can be extended, and here, we show the result true for n = 4 by proving there are infinitely many sets of four integers with four common factor differences.

Original language | English (US) |
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Pages (from-to) | 1059-1068 |

Number of pages | 10 |

Journal | International Journal of Number Theory |

Volume | 15 |

Issue number | 5 |

DOIs | |

State | Published - Jun 1 2019 |

## Keywords

- Erdös problem
- common factor difference
- elliptic curve

## ASJC Scopus subject areas

- Algebra and Number Theory