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

Abe, Nobuhisa

Abe, Nobuhisa

Proc. Japan Acad. Ser. A Math. Sci., Tome 76 (2000) no. 10, p. 16-17 / Harvested from Project Euclid

Résumé

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.

Publié le : 2000-02-14
Classification: Diophantine equation, 11D

@article{1148393581,
     author = {Abe, Nobuhisa},
     title = {On the Diophantine equation $x(x + 1) \dotsm (x + n) + 1 = y^2$},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {76},
     number = {10},
     year = {2000},
     pages = { 16-17},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148393581}
}

Abe, Nobuhisa. On the Diophantine equation $x(x + 1) \dotsm (x + n) + 1 = y^2$. Proc. Japan Acad. Ser. A Math. Sci., Tome 76 (2000) no. 10, pp.  16-17. http://gdmltest.u-ga.fr/item/1148393581/