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Topic: ----- ----- Pythagorous Theorem
Replies: 9   Last Post: Jul 17, 2013 4:18 PM

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Deep Deb

Posts: 420
Registered: 12/6/04
----- ----- Pythagorous Theorem
Posted: Jul 15, 2013 8:15 AM
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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.

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