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November 17th, 2018, 06:53 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 394 Thanks: 27 Math Focus: Number theory  Pythagorean ntuples' tendency
The following Pythagorean ntuples determine the set of every value for the exclusive sums of n terms in Pythagorean equations: For instance, Onetuples: x^2; 1, 4, 9, 16, 25, 36... Twotuples: x^2+y^2; 2, 5, 8, 10, 13, 18... Threetuples: x^2+y^2+ z^2; 3, 6, 9, 11, 12, 14... etc. Do these Pythagorean ntuples' frequencies together tend to converge or diverge toward infinity, or otherwise have a finite mode, either minimum or maximum? Last edited by Loren; November 17th, 2018 at 07:00 PM. Reason: To change one word 
November 18th, 2018, 04:53 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,105 Thanks: 1907 
For ntuples, the first number listed is n. What do you mean by "frequencies"?

November 18th, 2018, 10:21 AM  #3 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 394 Thanks: 27 Math Focus: Number theory 
The "frequency" here is the mode (minimum or maximum, for finite frequency) or cardinality (for transfinite frequency) of how often a sum appears as n approaches infinity. E.g., in the incomplete list below, 9 appears twice. Perhaps Cantor's diagonalization argument could be applied to the complete list. 

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ntuples, pythagorean, tendency 
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