The method of infinite ascent applied on $A^4 \pm n B^3 = C^2$

Title:

The method of infinite ascent applied on $A^4 \pm n B^3 = C^2$

Creator:

Jena, Susil Kumar

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:5dd3d29d-ddd1-4e32-8949-9baba10af7fc
uuid:5dd3d29d-ddd1-4e32-8949-9baba10af7fc

Subject:

method of infinite ascent and Diophantine equation $A^4 \pm nB^3 = C^2$

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Each of the Diophantine equations $A^4 \pm nB^3 = C^2$ has an infinite number of integral solutions $(A, B, C)$ for any positive integer $n$. In this paper, we will show how the method of infinite ascent could be applied to generate these solutions. We will investigate the conditions when $A$, $B$ and $C$ are pair-wise co-prime. As a side result of this investigation, we will show a method of generating an infinite number of co-prime integral solutions $(A, B, C)$ of the Diophantine equation $aA^3 + cB^3 = C^2$ for any co-prime integer pair $(a,c)$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

369-374

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:2

Harvested from:

CDK

Metadata only:

false