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I made a contribution to this article little more than a week ago on "the universal set of Pythagorean triples." Someone removed it. Why? I made reference to an article that contains rigorous proof of a matrix of Pythagorean triples that form the universal set of triples. This is the ultimate in finding the triples. Why was it removed, and what must I do right this time to have it maintained? Should I rather write my own article, independent on this one, for finding any Pythagorean triple? <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/119.46.251.60|119.46.251.60]] ([[User talk:119.46.251.60|talk]]) 07:59, 6 December 2013 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->
: Please see the page [[WP:OR]]. The short summary is that Wikipedia does not publish original research, and that's what you were adding to the page. (Also, for what it's worth, your method is a relatively minor variation of some of the formulas on this page; for example, if we set ''x'' = ''m''/''n'' and rescale then your triple is the same as the "usual" triple from [[Pythagorean_triple#Generating_a_triple|Euclid's formula]].) --[[User:Joel B. Lewis|JBL]] ([[User_talk:Joel_B._Lewis|talk]]) 19:35, 6 December 2013 (UTC)
== Generating triples when one side is known ==
This section is wrong so someone should fix it:) Euclid's formula is designed to generate only primitive triples, but the text claims that it will generate all of them. Omitting the restriction that m and n should be coprime allows some non-primitive triples to be generated, but not all of them. E.g. in the example given with b = 24, (18, 24, 30) and various others are missed. In order to generate all possible triples, the factor k as in http://en.wikipedia.org/wiki/Pythagorean_triple#Generating_a_triple needs to be included.
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