login
A291420
Numbers n such that there exist exactly four distinct Pythagorean triangles, at least one of them primitive, with area n.
0
341880, 8168160, 14636160, 17957940, 52492440, 116396280, 1071572040, 1187525640, 1728483120, 5988702720, 6609482880, 22539095040, 29239970760, 136496680320, 258670630680, 398648544840, 494892478080, 592003418160, 1329673884000, 1343798407560, 2190884461920
OFFSET
1,1
COMMENTS
Numbers n such that there exist positive integers x, y with x > y and n = x*y*(x-y)*(x+y).
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.
EXAMPLE
p^2 - p*q + q^2 = r^2;
p = 208, q = 418, r = 362, q - p = 210;
n = p*r*q*(q-p) = 208*418*362*210 = 6609482880.
x = 640, y = 627 gives the same area:
n = x*y*(x-y)*(x+y) = 640*627*13*1267 = 6609482880.
KEYWORD
nonn
AUTHOR
Sture Sjöstedt, Aug 23 2017
EXTENSIONS
a(12)-a(21) from Giovanni Resta, Aug 28 2017
STATUS
approved