A Classroom Note on: Bounds on Integer Solutions of xy = k(x + y) and xyz = k(xy + xz + yz)

Diophantine equations constitute a rich mathematical field. This article may be useful as a basis for a student math club project. There are several situations in which one needs to find a solution of indeterminate polynomial equations that allow the variables to be integers only. These indeterminat...

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Bibliographic Details
Published in:Mathematics and computer education 2011-04, Vol.45 (2), p.141
Main Authors: Umar, Abdullahi, Alassar, Rajai
Format: Article
Language:English
Subjects:
Clubs
College Mathematics
Equations (Mathematics)
Mathematical problems
Mathematics education
Mathematics Instruction
Polynomials
Problem Solving
Variables
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Summary:Diophantine equations constitute a rich mathematical field. This article may be useful as a basis for a student math club project. There are several situations in which one needs to find a solution of indeterminate polynomial equations that allow the variables to be integers only. These indeterminate equations are fewer than the involved unknown variables. Such problems are special cases of the general class of problems known as Diophantine equations. These equations are interesting because they are usually connected to some mathematical object of interest, such as the classical example when the lengths of the sides of a box are required to be integers and the surface area to be equal to its volume. In this article, the authors discuss the more general problems xy = k(x + y) and xyz = k(xy + xz + yz) in which x, y, z, and k are positive integers. (Contains 1 figure and 3 tables.)
ISSN:0730-8639