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%I A370777 #12 Apr 20 2024 10:30:53
%S A370777 1,2,2,3,1,4,8,9,1,6,18,19,1,8,32,33,1,10,50,51,1,12,72,73,1,14,98,99,
%T A370777 1,16,128,129,1,18,162,163,1,20,200,201,1,22,242,243,1,24,288,289,1,
%U A370777 26,338,339,1,28,392,393,1,30,450,451,1,32,512,513,1,34,578,579,1,36,648,649,1,38,722,723,1,40,800,801
%N A370777 Table read by rows: row n is the unique primitive Pythagorean quadruple (a,b,c,d) such that (a+b+c-d)/2 = n and a+c=d.
%C A370777 A Pythagorean quadruple is a quadruple (a,b,c,d) of positive integers such that a^2 + b^2 + c^2 = d^2 with a <= b <= c. Its inradius is (a+b+c-d)/2, which is a positive integer.
%D A370777 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.
%H A370777 Miguel-Ángel Pérez García-Ortega, <a href="/A370777/a370777.pdf">Cuaternas pitagóricas</a>
%F A370777 Row n = (a, b, c, d) = (1, 2*n, 2*n^2, 2*n^2 + 1).
%e A370777 Table begins:
%e A370777   n=1:   1,   2,   2,   3;
%e A370777   n=2:   1,   4,   8,   9;
%e A370777   n=3:   1,   6,  18,  19;
%e A370777   n=4:   1,   8,  32,  33;
%e A370777   n=5:   1,  10,  50,  51;
%t A370777 cuaternas={};Do[cuaternas=Join[cuaternas,{1,2n,2n^2,2n^2+1}],{n,1,35}];cuaternas
%K A370777 nonn,easy,tabf
%O A370777 1,2
%A A370777 _Miguel-Ángel Pérez García-Ortega_, Mar 01 2024

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