1. The method of infinite ascent applied on $A^4 \pm n B^3 = C^2$
- Creator:
- Jena, Susil Kumar
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- method of infinite ascent and Diophantine equation $A^4 \pm nB^3 = C^2$
- Language:
- English
- 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 $(a,c)$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public