Thanks heaps but there is another one which I cant figure out. I have to prove that for each positive integer n there exist integers x,y,z > 1 so that:
x^2+y^2=17z^(4n)
:S
How does induction work with 4 variables?
Why do you worry about the variables? Worry about n...
For $\displaystyle n = 1:\,\,4^2+1^2=17\cdot 1^{4}$...check
Suppose for $\displaystyle n:\,\,\exists x,y,z\,\,s.t.\,\,x^2+y^2=17z^{4n}$ , and we shall prove for n+1. But
$\displaystyle z^{4(n+1)}=z^4z^{4n}$ , so using the inductive hypothesis...
Tonio