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

Jena, Susil Kumar. "The method of infinite ascent applied on $A^4 \pm n B^3 = C^2$." Czechoslovak Mathematical Journal 63.2 (2013): 369-374. <http://eudml.org/doc/260615>.

@article{Jena2013,
abstract = {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 $(a,c)$.},
author = {Jena, Susil Kumar},
journal = {Czechoslovak Mathematical Journal},
keywords = {method of infinite ascent; Diophantine equation $A^4 \pm nB^3 = C^2$; method of infinite ascent; quartic Diophantine equation},
language = {eng},
number = {2},
pages = {369-374},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The method of infinite ascent applied on $A^4 \pm n B^3 = C^2$},
url = {http://eudml.org/doc/260615},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Jena, Susil Kumar
TI - The method of infinite ascent applied on $A^4 \pm n B^3 = C^2$
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 369
EP - 374
AB - 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 $(a,c)$.
LA - eng
KW - method of infinite ascent; Diophantine equation $A^4 \pm nB^3 = C^2$; method of infinite ascent; quartic Diophantine equation
UR - http://eudml.org/doc/260615
ER -