×

On the Diophantine equation \(x(x+1) \cdots (x+n)+1= y^2\) \((17\leq n= \text{odd}\leq 27)\). (English) Zbl 1186.11014

Summary: We consider the Diophantine equation as mentioned in the title and solve it completely, i.e., show that there exist no integer solution satisfying this equation.

MSC:

11D41 Higher degree equations; Fermat’s equation
11Y50 Computer solution of Diophantine equations
PDFBibTeX XMLCite
Full Text: DOI Euclid

References:

[1] Abe, N.: On the Diophantine equation \(x(x+1)\cdots(x+n)+1=y^2\). Proc. Japan Acad., 76A , 16-17 (2000). · Zbl 0996.11022 · doi:10.3792/pjaa.76.16
[2] Erdös, P., and Selfridge, J. L.: The product of consecutive integers is never a power. Illinois J. Math., 19 , 292-301 (1975). · Zbl 0295.10017
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.