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
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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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