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%I #44 Nov 05 2021 17:30:55
%S 341880,8168160,14636160,17957940,52492440,116396280,1071572040,
%T 1187525640,1728483120,5988702720,6609482880,22539095040,29239970760,
%U 136496680320,258670630680,398648544840,494892478080,592003418160,1329673884000,1343798407560,2190884461920
%N Numbers n such that there exist exactly four distinct Pythagorean triangles, at least one of them primitive, with area n.
%C Numbers n such that there exist positive integers x, y with x > y and n = x*y*(x-y)*(x+y).
%C Many of them consist of a Pythagorean triangle plus a triple which is a solution to Carroll's problem: Find three Pythagorean triangles with the same area.
%e p^2 - p*q + q^2 = r^2;
%e p = 208, q = 418, r = 362, q - p = 210;
%e n = p*r*q*(q-p) = 208*418*362*210 = 6609482880.
%e x = 640, y = 627 gives the same area:
%e n = x*y*(x-y)*(x+y) = 640*627*13*1267 = 6609482880.
%Y Cf. A009127, A024407, A055193, A088513, A088977, A089025, A177021, A291591.
%K nonn
%O 1,1
%A _Sture Sjöstedt_, Aug 23 2017
%E a(12)-a(21) from _Giovanni Resta_, Aug 28 2017
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