Julius Fergy T. Rabago and Richard P. Tagle

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

Volume 19, 2013, Number 3, Pages 28—32

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## Details

### Authors and affiliations

Julius Fergy T. Rabago

*Faculty, Department of Mathematics and Physics
College of Arts and Sciences, Central Luzon State University
Science City of Muñoz 3 120, Nueva Ecija, Philippines*

Richard P. Tagle

*Faculty, Department of Mathematics and Physics
College of Arts and Sciences, Central Luzon State University
Science City of Muñoz 3 120, Nueva Ecija, Philippines*

### Abstract

In this paper, we study some elementary problems involving surface area and volume of a certain regular solid. In particular, we find integral dimensions of a rectangular prism in which its surface area and volume are numerically equal. The problem leads us in solving a specific case of the well-known Diophantine problem

### Keywords

- Solids
- Diophantine equation
- Egyptian fraction
- Integral solutions

### AMS Classification

- 11D68
- 11A07

### References

- Guy, R. K. Unsolved Problems in Number Theory, 2nd Ed., Springer, Verlag, New York, 1994.
- Ionascu, E. J., A. Wilson, On the Erdős–Straus Conjecture, Rev. Roumaine Math. Pures Appl., Vol. 56, 2011, No. 1, 21–30.
- Kishan, H., M. Rani, S. Agarwal, The Diophantine Equations of Second and Higher Degree of the form 3xy = n(x + y) and 3xyz = n(xy + yz + xz) etc, Asian J. of Algebra, Vol. 4, 2011, No. 1, 31–37.
- Monks, M., A. Velingker. On the Erdős–Straus Conjecture: Properties of Solutions to its Underlying Diophantine Equation (preprint).
- Zelator, K. An ancient Egyptian problem: The diophantine equation 4/n = 1/x + 1/y + 1/z (preprint).

## Related papers

## Cite this paper

APARabago, J. F. T., & Tagle, R. P. (2013). On the area and volume of a certain regular solid and the Diophantine equation 1/2 = 1/x + 1/y + 1/z. Notes on Number Theory and Discrete Mathematics, 19(3), 28-32.

ChicagoRabago, Julius Fergy T., and Richard P. Tagle. “On the Area and Volume of a Certain Regular Solid and the Diophantine Equation 1/2 = 1/x + 1/y + 1/z.” Notes on Number Theory and Discrete Mathematics 19, no. 3 (2013): 28-32.

MLARabago, Julius Fergy T., and Richard P. Tagle. “On the Area and Volume of a Certain Regular Solid and the Diophantine Equation 1/2 = 1/x + 1/y + 1/z.” Notes on Number Theory and Discrete Mathematics 19.3 (2013): 28-32. Print.