Susil Kumar Jena

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 20, 2014, Number 2, Pages 29—34

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## Details

### Authors and affiliations

Susil Kumar Jena

*Department of Electronics and Telecommunication Engineering
KIIT University
Bhubaneswar 751024, Odisha, India*

### Abstract

We give parametric solutions, and thus show that the two Diophantine equations 2*A*^{6} + *B*^{6} = 2*C*^{6} ± *D*^{3} have infinitely many nontrivial and primitive solutions in positive integers (*A, **B*, *C*, *D*).

### Keywords

- Diophantine equation
- Diophantine equation 2
*A*^{6}+*B*^{6}= 2*C*^{6}+*D*^{3} - Diophantine equation 2
*A*^{6}+*B*^{6}= 2*C*^{6}−*D*^{3} - Equal sums of higher powers

### AMS Classification

- 11D41
- 11D72

### References

- Bremner, A. A geometric approach to equal sums of sixth powers, Proc. London Math. Soc., Vol. 43, 1981, 544–581.
- Brudno, S. On generating infinitely many solutions of the Diophantine equation A
^{6}+ B^{6}+ C^{6}= D^{6}+ E^{6}+ F^{6}, Math. Comp., Vol. 24, 1970, 453–454. - Brudno, S. Triples of sixth powers with equal sums, Math. Comp., Vol. 30, 1976, 646–648.
- Choudhry, A. On equal sums of sixth powers, Indian J. Pure Appl. Math., Vol. 25, 1994, 837–841.
- Choudhry, A. On equal sums of sixth powers, Rocky Mountain J. Math., Vol. 30, 2000, 843–848.
- Delorme, J.-J. On the Diophantine equation , Math. Comput., Vol. 59, 1992, 703–715.

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## Cite this paper

APAKumar Jena, S. (2014). On two Diophantine equations 2A^{6} + B^{6} = 2C^{6} ± D^{3}. Notes on Number Theory and Discrete Mathematics, 20(2), 29-34.

Kumar Jena, Susil. “On Two Diophantine Equations 2A^{6} + B^{6} = 2C^{6} ± D^{3}.” Notes on Number Theory and Discrete Mathematics 20, no. 2 (2014): 29-34.

Kumar Jena, Susil. “On Two Diophantine Equations 2A^{6} + B^{6} = 2C^{6} ± D^{3}.” Notes on Number Theory and Discrete Mathematics 20.2 (2014): 29-34. Print.