On the area and volume of a certain regular solid and the Diophantine equation 1/2 = 1/x + 1/y + 1/z

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
Full paper (PDF, 147 Kb)

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

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