A problem of Erdös-Graham-Granville-Selfridge on integral points on hyperelliptic curves

Hung Bui, Kyle Pratt, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

Erdos, Graham, and Selfridge considered, for each positive integer n, the least value of tnso that the integers n+1, n+2, . . . , n+tn 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 tn, and in the process solve Granville’s problem unconditionally.
Original languageEnglish
Pages (from-to)309-323
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume176
Publication statusPublished - Feb 2024

Keywords

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

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