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Thursday 23 Mar 2023Algebra and Number Theory Seminar: A problem of Erdos-Graham-Granville-Selfridge on integral points on hyperelliptic curves

Dr Kyle Pratt - University of Oxford

Harrison 203 14:30-16:30

Abstract: Erdos, Graham, and Selfridge considered, for each positive integer $n$, the least value of $t_n$ so that the integers $n+1, n+2, \dots, 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 $t_n$, 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 $t_n$, including an unconditional resolution of Granville's problem.

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