Susil Kumar Jena

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

Volume 19, 2013, Number 2, Pages 10—14

**Download full paper: PDF, 124 Kb**

## Details

### Authors and affiliations

Susil Kumar Jena

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

### Abstract

In this paper we will produce different formulae for which the Diophantine equation *A*^{3} ± *nB*^{2} = *C*^{3} will generate infinite number of co-prime integral solutions for (*A*, *B*, *C*) for any positive integer *n*.

### Keywords

- Method of infinite ascent
- Diophantine equations
*A*^{3}±*nB*^{2}=*C*^{3}

### AMS Classification

- 11D41

### References

- Beukers, F. The Diophantine equation Ax
^{p}+ By^{q}= Cz^{r}, Duke Math. J., Vol. 91, 1998, 61–88. - Bruin, N. On powers as sums of two cubes, ANTS IV, Leiden, 2000, Lecture Notes in Comp. Sci., Springer, Vol. 1838, 2000, 169–184.
- Bruin, N. Chabauty methods using elliptic curves, J. reine angew. Math., Vol. 562, 2003, 27–49.
- Jena, S. K. Method of Infinite Ascent applied on mA
^{6}+ nB^{3}= C^{2}, The Math. Stud., Vol. 77, 2008, No. 1–4, 239–246. - Jena, S. K. Method of Infinite Ascent applied on A
^{4}± nB^{2}= C^{3}, The Math. Stud., Vol. 78, 2009, No. 1–4, 233–238. - Jena, S. K. Method of Infinite Ascent applied on mA
^{3}+ nB^{3}= C^{2}, The Math. Stud., Vol. 79, 2010, No. 1–4, 187–192. - Jena, S. K. Method of Infinite Ascent applied on mA
^{3}+ nB^{3}= 3C^{2}, The Math. Stud., Vol. 81, 2012, No. 1–4 (To appear). - Kraus, A. Sur l’equation a
^{3}+ b^{3}= c^{p}, Experiment Math. J., Vol. 71, 1998, No. 1, 1–13. 14

## Related papers

## Cite this paper

APAJena, S. K. (2013). Method of infinite ascent applied on *A*^{3} ± *nB*^{2} = *C*^{3}. Notes on Number Theory and Discrete Mathematics, 19(2), 10-14.

Jena, Susil Kumar. “Method of Infinite Ascent Applied on *A*^{3} ± *nB*^{2} = *C*^{3}.” Notes on Number Theory and Discrete Mathematics 19, no. 2 (2013): 10-14.

Jena, Susil Kumar. “Method of Infinite Ascent Applied on *A*^{3} ± *nB*^{2} = *C*^{3}.” Notes on Number Theory and Discrete Mathematics 19.2 (2013): 10-14. Print.