Manchester Number Theory Seminar - Hung Bui
| Dates: | 7 March 2023 |
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| Times: | 15:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Hung Bui (University of Manchester)
Title: Brocard-Ramanujan's problem on polynomial-factorial equations
Abstract: Brocard and Ramanujan, independently, posed the problem of finding all integer solutions to the equation n! + 1 = x^2. It is conjectured that the only solutions are n = 4,5,7. More generally, one may ask about integer solutions to the polynomial-factorial equation n! = P(x), where P is an integer polynomial of degree at least 2. Berend and Osgood showed that the set of n for which the equation has an integer solution x is of density 0, which answered a question of Erdos. We improve on this result of Berend and Osgood, obtaining a power saving bound for the number of solutions of a polynomial-factorial equation. This is joint work with Kyle Pratt and Alexandru Zaharescu.
Room: Frank Adams 1
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Frank Adams 1
Alan Turing Building
Manchester
