The problem is as follows:

------------------------------------

We all know that this is the Fibonacci recusion.

F_{n }= F_{n-1 }+ F_{n-2}, F_{0 }= 1 , F_{1} = 1

How to prove that the following triple (x,y,z) follow Pythagorean Theorem ?

x = (F_{i}) x (F_{i+3})

y = 2 x (F_{i+1}) x (F_{i+2})

z = (F_{i+1})^{2}+ (F_{i+2})^{2}