Mathematics

Dr. Shanta Laishram
Indian Statistical Institute, Delhi

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. In my talk, I will give a brief survey of the problem and highlight some of the techniques in the proof. The talk will be accessible to a general mathematical audience. This is a joint work with Hajdu and Tengely of University of Debrecen, Hungary.