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.

Old Original Oskar!'s approach does show that there are an infinite number of solutions, thus providing an answer for (B).  To give an answer to (A), the following are three solutions:

x = 1024
y = 16
z = 128

x = 33554432
y = 1024
z = 131072

x = 1099511627776
y = 65536
z = 134217728

Posted by Dej Mar on 2006-09-15 13:15:57