On equal products of consecutive integers
Nguyen Xuan Tho
Hanoi University of Science and Technology, Vietnam

Abstract
In 1970, Macleod and Barrodale [Canad. Math. Bull. 13 (1970), 255–259] conjectured that the equation has no solutions in the positive integers if and . In 1990, Saradha and Shorey [Proc. Indian Acad. Sci. Math. Sci. 100 (1990), no. 2, 107–132, Theorem 3] showed that this equation has no solutions in the positive integers if . However, Saradha and Shorey’s proof is quite involved. In this paper, we give an elementary proof to Saradha and Shorey’s theorem.
Cite this article
Nguyen Xuan Tho, On equal products of consecutive integers. Elem. Math. (2025), published online first
DOI 10.4171/EM/556