Note on a paper "An Extension of a Theorem of Euler" by Hirata-Kohno et al

In this paper we extend a result of Hirata-Kohno, Laishram, Shorey and Tijdeman on the Diophantine equation $n(n+d)\mathrm{.}\mathrm{.}\mathrm{.}(n+(k-1)d)=b{y}^2,$ where $n,d,k\ge 2$ and $y$ are positive integers such that $\gcd (n,d)=1.$