Prove that the equation x^2+y^2=z^5 has an infinite number of positive integer solutions.
(In reply to
Another set by Larry)
Your infinite set is just a small portion of one of mine.
The first few you give are:
4, 4, 2
25, 50, 5
100, 300, 10
i=1,2,3
I consider these examples of one of mine:
For any a,b,c that satisfies a^2 + b^2 = c
(ac^(5n+2))^2 +
(bc^(5n+2))^2 = (c^(2n+1))^5
a=1, b=1, c=2, n=0
a=1, b=2, c=5, n=0
a=1, b=3, c=10, n=0
In your equation J=i^2+1, J=c, i=b, 1=a
My n is your implied 0 (2n+1=1)

Posted by Jer
on 20100512 16:53:19 