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)
The question asks us specifically to prove the proposition using simple induction. But, Unbeatable0, if I've taken your hint correctly, the values for x, y & z need to be greater than 1.
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...
Why do you worry about the variables? Worry about n...
For ...check
Here, you should worry about the variables, because the question specifies integers x,y,z > 1. (But it's not hard to adapt the base case example to satisfy those conditions.)
Here, you should worry about the variables, because the question specifies integers x,y,z > 1. (But it's not hard to adapt the base case example to satisfy those conditions.)
Good point. Completely missed that bigger than 1 thingy.