  In this work, we accomplish three goals. First, we determine the entire
family of positive integer solutions to the three- variable Diophantine
equation, xy=z^2; for n=2,3,4,5,6. For n=2, we obtain a 3-parameter family of
solutions; for n=3, a 5-parameter of solutions; likewise for n=4. For n=5, a
7-parameter family of solutions; and likewise for n=6. See Theorems 2 through 6
respectively. The second goal of this paper, is determining all the positive
integer solutions of xyz=w^2. This is done in Theorem7; the solution set is
described in terms of six independent parameters. Finally, in Theorem 8, we
achieve our third goal: determining all the positive integer solutions of the
5-variable Diophantine system: xy=v^2 and yz=w^2. The solution set is expressed
in terms of eight parameters. This paper contains a total of four references.
