## Abstract

Erdos, Graham, and Selfridge considered, for each positive integer n, the least value of

*t*so that the integers_{n}*n*+1,*n*+2, . . . ,*n*+t_{n}contain a subset the product of whose members with n is a square. An open problem posed by Granville concerns the size of tn, under the assumption of the ABC Conjecture. We establish some results on the distribution of t_{n}, and in the process solve Granville’s problem unconditionally.Original language | English |
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Pages (from-to) | 309-323 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 176 |

Publication status | Published - Feb 2024 |

## Keywords

- squares
- largest prime factor
- smooth numbers
- hyperelliptic curves
- integral points