Primitive pythagorean n-tuple tree

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Author(s):
Subject: Number Theory
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Recomm. for undergrads: no
Posted by: tsihonglau
on: April 24th, 2011

\begin{conjecture} Find linear transformation construction of primitive pythagorean n-tuple tree! % Enter your conjecture in LaTeX % You may change "conjecture" to "question" or "problem" if you prefer. \end{conjecture}

% You may use many features of TeX, such as % arbitrary math (between $...$ and $$...$$) % \begin{theorem}...\end{theorem} environment, also works for question, problem, conjecture, ... % % Our special features: % Links to wikipedia: \Def {mathematics} or \Def[coloring]{Graph_coloring} % General web links: \href [The On-Line Encyclopedia of Integer Sequences]{http://www.research.att.com/~njas/sequences/} 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.

\href [There are at least two known linear transformation construction of primitive pythagorean triple tree!]{http://home.educities.edu.tw/tsihonglau/senior/primitive_pythagorean_triple_ternary_tree.html}

\href [Wikipedia]{http://en.wikipedia.org/wiki/Pythagorean_triple#Parent.2Fchild_relationships}

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

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

Bibliography

% Example: %*[B] Claude Berge, Farbung von Graphen, deren samtliche bzw. deren ungerade Kreise starr sind, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 10 (1961), 114. % %[CRS] Maria Chudnovsky, Neil Robertson, Paul Seymour, Robin Thomas: \arxiv[The strong perfect graph theorem]{math.CO/0212070}, % Ann. of Math. (2) 164 (2006), no. 1, 51--229. \MRhref{MR2233847} % % (Put an empty line between individual entries)


* indicates original appearance(s) of problem.