MATH 319 Assignment #2

Due Monday, February 10

In this exploratory assignment you will be looking for solutions to the equation , where x,y, and z are positive integers. Clearly (0,0,0), (1,0,1), and (0,1,1) are solutions but they are not very interesting. There are infinitely many different solutions. Many of the solutions are related to each other in a simple way.

a) Find ten different solutions. Interchanging the roles of x and y does not count as a different solution. Having a computer search for solutions is probably the best way to do this. Maple will work very well here. I have put a Maple program called Sum of Cubes Equals a Square in my outbox that will find solutions. (See me about getting to this program if you have trouble.)

b) Suppose that (a,b,c) is a solution. Show that if x is a positive integer then (ax²,bx²,cx³) is another solution.

c) A solution (u,v,w) is said to be primitive if it cannot be written as (ax²,bx²,cx³) for any solution (a,b,c) and x > 1. Which of the solutions you found in a) are primitive?