Cubes from products of terms in progression with one term missing

Kyle Pratt

Let $5\le k\le 11$ and $0\le i\le k-1$ be integers. We determine all solutions to the equation \begin{align*} n(n+d)(n+2d)\cdots(n+(i-1)d)(n+(i+1)d) \cdots (n+(k-1)d) = y^3…