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y - 2x - a = 0, y^2 - xy + x^2 - b = 0,. NT system

Source: Eotvos 1917 p1

September 10, 2024
number theorysystem of equationsdiophantineDiophantine equation

Problem Statement

If aa and bb are integers and if the solutions of the system of equations y−2x−a=0y - 2x - a = 0 y2−xy+x2−b=0y^2 - xy + x^2 - b = 0 are rational, prove that the solutions are integers.
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