# Manchester Number Theory Seminar - Hung Bui

Dates: | 7 March 2023 |
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Times: | 15:00 - 16:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Current University students |

Speaker: Hung Bui (University of Manchester)

Title: EGGS, squares and integer points on hyperelliptic curves

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, ..., 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 Kyle Pratt and Alexandru Zaharescu, in which we establish some results on the distribution of t_n, including an unconditional resolution of Granville's problem.

Room: Frank Adams 1