The resolution of the Diophantine equation \(x(x+d) \dots (x+(k-1)d) = by^2\) for fixed \(d\) (Q2717622)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The resolution of the Diophantine equation \(x(x+d) \dots (x+(k-1)d) = by^2\) for fixed \(d\) |
scientific article; zbMATH DE number 1605217
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The resolution of the Diophantine equation \(x(x+d) \dots (x+(k-1)d) = by^2\) for fixed \(d\) |
scientific article; zbMATH DE number 1605217 |
Statements
17 June 2001
0 references
products of terms in arithmetical progressions
0 references
0.89605975
0 references
0.8958957
0 references
0.8956615
0 references
The resolution of the Diophantine equation \(x(x+d) \dots (x+(k-1)d) = by^2\) for fixed \(d\) (English)
0 references
The theme of this paper is the equation NEWLINE\[NEWLINE x(x+d)\cdots (x+(k-1)d)=by^2 \tag{1}NEWLINE\]NEWLINE with \(d>1\), \(k\geq 3\), \(\gcd(x,d)=1\), \(x\) and \(y\) positive and where the greatest prime factor of \(b\) is \({}\leq k\). \textit{N. Saradha} [Acta Arith. 86, No. 1, 27-43 (1998; Zbl 0920.11018)] gave an algorithm to solve (1) for fixed \(d\) and treated the cases \(d<23\). The authors solve (1) for \(23\leq d \leq 30\).
0 references
