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.)