Improved exponent bounds for Erdős--Selfridge curves

Pranabesh Das, Kyle Pratt

Given integers $k,\ell \ge 2$, define the Erdős--Selfridge curve \begin{align*} \mathcal{C}_{k,\ell} : y^\ell = x(x+1)\cdots (x+k-1). \end{align*} Bennett and Siksek proved that i…