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Parametric Solutions of the Diophantine Equation $A^2 + nB^4 = C^3$

Volume 62 / 2014

Susil Kumar Jena Bulletin Polish Acad. Sci. Math. 62 (2014), 211-214 MSC: Primary 11D41; Secondary 11D72. DOI: 10.4064/ba62-3-2

Abstract

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.

Authors

  • Susil Kumar JenaDepartment of Electronics & Telecommunication Engineering
    KIIT University, Bhubaneswar 751024
    Odisha, India
    e-mail

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