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Numerators (denominators are all 840) of x-coordinates of four points on the parabola y = x^2, x >= 0, at rational distances (distance between any two points is rational).
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%I #11 Aug 21 2018 10:17:56

%S 475,551,799,3076

%N Numerators (denominators are all 840) of x-coordinates of four points on the parabola y = x^2, x >= 0, at rational distances (distance between any two points is rational).

%F The distance formula between points on the parabola y = x^2.

%e We need 6 Pythagorean triples such that the ratios of the sides satisfies

%e (a+d = b+f = c+e) where x1+x2 = a, x2+x3 = b, x1+x3 = c, x3+x4 = d

%e (45/28 + 3551/840 = 171/140 + 775/168 = 91/60 + 1209/280). Solve for x1,x2,... to get the sequence.

%K nonn,full,fini

%O 0,1

%A T. Haj (t.haj(AT)sbcglobal.net), Apr 21 2005