On equal products of consecutive integers

  • Nguyen Xuan Tho

    Hanoi University of Science and Technology, Vietnam
On equal products of consecutive integers cover
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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