On the Diophantine equation $x(x + 1) \dotsm (x + n) + 1 = y^2$

Nobuhisa Abe

doi:10.3792/pjaa.76.16

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Feb. 2000 On the Diophantine equation $x(x + 1) \dotsm (x + n) + 1 = y^2$

Nobuhisa Abe

Proc. Japan Acad. Ser. A Math. Sci. 76(2): 16-17 (Feb. 2000). DOI: 10.3792/pjaa.76.16

Abstract

Let $\mathbf{N}$ denote the set of natural numbers $\{1, 2, 3, \ldots\}$. $n$ being an odd natural number, we consider the Diophantine equation as mentioned in the title and solve it completely for $n \leq 15$, i.e. find all $(x,y) \in \mathbf{N}^2$ satisfying this equation.

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Nobuhisa Abe. "On the Diophantine equation $x(x + 1) \dotsm (x + n) + 1 = y^2$." Proc. Japan Acad. Ser. A Math. Sci. 76 (2) 16 - 17, Feb. 2000. https://doi.org/10.3792/pjaa.76.16