Primitive pythagorean n-tuple tree

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Subject: Number Theory
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Recomm. for undergrads: no
Posted by: tsihonglau
on: April 24th, 2011
Conjecture   Find linear transformation construction of primitive pythagorean n-tuple tree!

Primitive pythagorean n-tuple is a n-tuple $ (a_{1},a_{2},a_{3},...,a_{n}) $ such that $ a_{1}^2 + a_{2}^2 + a_{3}^2 + ... + a_{n-1}^2 = a_{n}^2 $

and the greatest common divisor of $ (a_{1},a_{2},a_{3},...,a_{n}) $ is 1.

There are at least two known linear transformation construction of primitive pythagorean triple tree!

Wikipedia

Is there any other linear transformation construction of primitive pythagorean triple tree?

Moreover, find linear transformation construction of primitive pythagorean n-tuple tree!

Bibliography



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