Prove that the equation x^2+y^2=z^5 has an infinite number of positive integer solutions.
Not sure if this is included in any of the previous:
For all nonnegative integers i,
Let J=i^2 + 1
X=J^2
Y=sqrt(J^5  J^4) = i * J^2
Z=J
X^2 + Y^2 = J^4 + J^5  J^4 = J^5 = Z^5
The first few are:
4, 4, 2
25, 50, 5
100, 300, 10
Edited on May 11, 2010, 11:23 pm
Edited on May 11, 2010, 11:34 pm

Posted by Larry
on 20100511 23:23:09 