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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Pythegoros_Theorem
Replies: 6   Last Post: Jul 26, 2012 1:28 PM

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david

Posts: 125
Registered: 8/3/08
Pythegoros_Theorem
Posted: Jul 25, 2012 2:47 PM
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To generate the Pythagoas triplets one uses the following formula.

c = x^2 + y^2; a = x^2 - y^2; b = 2xy where x, y are coprime integers
such that x + y is odd.
Then one gets a^2 + b^2 = c^2 (1)
(1) will generate infinitely many Pythagorian triplets a, b, c.
Question: Will x and y generate all the right triangles? Or can there
be some right triangles which can not be generated by the above set of
x,y
A simple reply and relevant references will be appreciated. An example
will be very helpful.

David

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