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y^2 = x^3 +bx+b^2, incribe a triangle with vertices of rational coordinates

Source: Spanish Mathematical Olympiad 1986 P5

August 2, 2018
rationalTrianglecoordinatesalgebraanalytic geometry

Problem Statement

Consider the curve Γ\Gamma defined by the equation y2=x3+bx+b2y^2 = x^3 +bx+b^2, where bb is a nonzero rational constant. Inscribe in the curve Γ\Gamma a triangle whose vertices have rational coordinates.
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