Theoretical Statistics and Mathematics Unit, ISI Delhi

Variations of Erd\H{o}s- Selfridge superelliptic curves and their rational points

by Pranabesh Das, Shanta Laishram and N. Saradha

For the superelliptic curves of the form
$$ (x+1) \cdots(x+i-1)(x+i+1)\cdots (x+k)=y^\ell$$
with $k \geq 3$ and $\ell \geq 2,$ a prime, for some values of $i$ in
the range $2\leq i\leq k,$ we bound $\ell< e^{3^k},$
as in a recent paper of Bennett and Siksek.

isid/ms/2016/14 [fulltext]

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