Alladi Ramakrishnan Hall

Rational points on Erd{\H o}s Selfridge superelliptic curve and its variants.

N. Saradha

CBS, Mumbai

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 also
trace some of the old results connected with the problem.