Consider the equation x^2+y^5=z^3 where x, y, and z, are positive integers.

(A) Can you give at least three solutions to it?
(B) Determine whether or not there is an infinite number of solutions.

Although, as previously shown, there are an infinite number of solutions, they are not limited to powers of 2. For example, x=10, y=3, z=7 and x=1242, y=9, z=117 both work.

Posted by Dennis on 2006-09-15 14:30:07