Parametric Solutions of the Diophantine Equation $A^2 + nB^4 = C^3$
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 62 (2014) no. 3, pp. 211-214
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The Diophantine equation $A^2 + nB^4 = C^3$ has infinitely many integral solutions $A, B, C$ for any fixed integer $n$. The case $n = 0$ is trivial. By using a new polynomial identity we generate these solutions, and then give conditions when the solutions are pairwise co-prime.
Keywords:
diophantine equation has infinitely many integral solutions fixed integer trivial using polynomial identity generate these solutions conditions solutions pairwise co prime
Affiliations des auteurs :
Susil Kumar Jena 1
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author = {Susil Kumar Jena},
title = {Parametric {Solutions} of the {Diophantine} {Equation} $A^2 + nB^4 = C^3$},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {211--214},
publisher = {mathdoc},
volume = {62},
number = {3},
year = {2014},
doi = {10.4064/ba62-3-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba62-3-2/}
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Susil Kumar Jena. Parametric Solutions of the Diophantine Equation $A^2 + nB^4 = C^3$. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 62 (2014) no. 3, pp. 211-214. doi: 10.4064/ba62-3-2
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