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

Authors

Kyle Pratt, Oxford University

Document Type

Lecture

Publication Date

2-7-2023

Abstract

Erdős, Graham, and Selfridge considered, for each positive integer n, the least value of tn so 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 discuss recent work, joint with Hung Bui and Alexandru Zaharescu, in which we establish some results on the distribution of tn, including an unconditional resolution of Granville’s problem.

Relational Format

presentation

Recommended Citation

Pratt, Kyle, "A problem of Erdős-Graham-Granville-Selfridge on integral points on hyperelliptic curves" (2023). Algebra/Number Theory Seminar. 9.
https://egrove.olemiss.edu/math_algebra_number_theory/9