MathDB

5

Part of 1986 Spain Mathematical Olympiad

Problems(1)

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

Source: Spanish Mathematical Olympiad 1986 P5

8/2/2018
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.
rationalTrianglecoordinatesalgebraanalytic geometry