Geodesic
The method of infinite ascent applied on $A^4 \pm n B^3 = C^2$
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 369-374 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $(a,c)$.
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 $(a,c)$.
DOI : 10.1007/s10587-013-0022-4
Classification : 11D41, 11D72
Keywords: method of infinite ascent; Diophantine equation $A^4 \pm nB^3 = C^2$ 
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     title = {The method of infinite ascent applied on $A^4 \pm n B^3 = C^2$},
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Jena, Susil Kumar. The method of infinite ascent applied on $A^4 \pm n B^3 = C^2$. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 369-374. doi: 10.1007/s10587-013-0022-4

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