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KöMaL problem A, 2023 Difficulty 6.0 National Olympiad Prove it Hungary
Prove that the only integer solution of the following system of equations is u = v = x = y = z = 0 u=v=x=y=z=0 u = v = x = y = z = 0 u v = x 2 − 5 y 2 uv=x^2-5y^2 uv = x 2 − 5 y 2 ( u + v ) ( u + 2 v ) = x 2 − 5 z 2 (u+v)(u+2v)=x^2-5z^2 ( u + v ) ( u + 2 v ) = x 2 − 5 z 2
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