
  Pythagorous Theorem
Posted:
Jul 15, 2013 8:15 AM


Consider (1) below:
x^(2n) + y^(2n) = z^(2n) (1)
where x, y, z are coprime integers, integer n > 0.
(1) can be written as (2)
(x^n)^2 + (y^n)^2 = (z^n)^2 (2)
By Pythagorous theorem (2) can be represented by the three sides of a right triangle XYZ where
YZ = x^n, ZX = y^n, XY = z^n
Observation:each of x^n, y^n, z^n will have now magnitude and direction.
My question: Can the three variables in x, y, z in (1) be treated as vectors not scalar?
Any helpful comment will be appreciated.

