Tuesday, January 29 2019
11:30 - 12:30

#### In a recent paper Bennett and Siksek showed that for integers $k \geq 2$ and $\ell\geq 2$ if the curve$$(x+1)\cdots (x+k-1)=y^\ell$$has a rational solution in $x$ and $y$ then$$\ell\leq e^{3^k}.$$In this talk we will consider some variants of the above curve and show that similar result is true. We will alsotrace some of the old results connected with the problem.

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