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?

Printable View

- April 3rd 2011, 05:42 PMAdamCDiophantine eq
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? - April 3rd 2011, 10:42 PMUnbeatable0
No need for induction. Try to guess a solution which will be valid for all (and dependent on ), using a single solution to .

(Sorry if this hint was too big) - April 5th 2011, 01:49 AMSalome
I think AdamC and I are in the same class ;-)

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. - April 5th 2011, 03:55 AMtonio
- April 5th 2011, 09:11 AMOpalg
- April 5th 2011, 02:31 PMtonio