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Primitive pythagorean n-tuple tree

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Subject: Number Theory
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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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Linear transformation of primitive pythagorean n-tuple

On June 16th, 2021 Anonymous says:

Is it true that for primitive pythagorean n-tuple (a_1, a_2...... a_n), if there are (n-2) even terms and 1 odd term in the summation side of the equation and a_n is odd, a linear transformation can be made? And can we find any such primitive pythagorean n-tuple where a_n is even?

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