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It is well-known that there is a trinary tree that contains every primitive Pythagorean triple exactly once. It even has a Wikipedia page.

Is there a similar tree that contains each primitive Pythagorean quadruple exactly once?

Mangara
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    It even has a math.SE answer, with more math the the Wikipedia page. See the paper by see Cass & Arpaia cited there for that and higher degree forms. Always search first before posting questions. – Bill Dubuque Feb 17 '21 at 01:20
  • Thanks for pointing out that answer! I did search, but clearly not widely enough. – Mangara Feb 17 '21 at 01:33
  • The tree never made sense to me but some quadruples you might play with are

    $$(3,4,12,13)\qquad (5,12,84,85)\qquad (7,25,312,313)\qquad (9,40,840,841)\ (11,60,1860,1861)\quad (13,84,132,157)\quad (15,8,144,145)\quad (15,112,6384,6385)\ (17,144,408,433)\quad (19,180,16380,16381)\quad (21,20,420,421)\quad (21,220,60,229)\ $$

     – poetasis Feb 18 '21 at 02:03

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You can find the answer in the following paper: http://math.colgate.edu/~integers/u73/u73.pdf

Markiff
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