Integer points of \(y^2=x^3-4x+1\) (Q1106254)
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: Integer points of \(y^2=x^3-4x+1\) |
scientific article; zbMATH DE number 4061320
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Integer points of \(y^2=x^3-4x+1\) |
scientific article; zbMATH DE number 4061320 |
Statements
Integer points of \(y^2=x^3-4x+1\) (English)
0 references
1988
0 references
The integer solutions \((x,y)\) with \(y>0\) of the cubic title equation are found -- there are 11 of these in all -- by working in the associated cubic field generated by a root of \(x^3-4x+1=0\). The calculations performed are based on factorization techniques and are rather tedious. As a corollary all triangular numbers are determined that are also product of three consecutive integers; there are 6 such numbers.
0 references
cubic Diophantine equation
0 references
elliptic curve
0 references
integer curve
0 references
integer points
0 references
cubic field
0 references
triangular numbers
0 references
product of three consecutive integers
0 references
