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Aix-Marseille Université
Institut de Mathématiques de Marseille (I2M) - UMR 7373
Site Saint-Charles : 3 place Victor Hugo, Case 19, 13331 Marseille Cedex 3
Site Luminy : Campus de Luminy - Case 907 - 13288 Marseille Cedex 9

Séminaire

Power values of sums of products of consecutive integers

Shanta Laishram
Indian Statistical Institute (ISI), Delhi Centre, New Delhi, India
https://www.isid.ac.in/~shanta/

Date(s) : 21/06/2016   iCal
11h00 - 12h00

The sum or the product of consecutive integers being a perfect power is well understood. However the question of sums of products of consecutive integers being a perfect power is a much more difficult problem. In this talk, we investigate this problem and give general finiteness results. Also, we give all solutions when the terms in the product considered is at most ten. The proof involves a combination of different techniques, ranging from linear forms in logarithms of algebraic numbers, Runge’s method, computing integral points on curves among others. This is a joint work with Hajdu and Tengely of University of Debrecen, Hungary.

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.707.143

 

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