关于不定方程组{x^2-2y^2=1 2y^2-3z^2=4和{x^2-2y^2=1 2y^2-5z^2=7

On the Systems of Diophantine Equations {x^2-2y^2=1 2y^2-3z^2=4 and {x^2-2y^2=1 2y^2-5z^2=7

对于不定方程组{x^2-2y^2=1 2y^2-3z^2=4和{x^2-2y^2=1 2y^2-5z^2=7证明了它们没有整数解.

This paper deals with the systems of diophantine equations{x^2-2y^2=1 2y^2-3z^2=4and{x^2-2y^2=1 2y^2-5z^2=7. It is proved that the integer solutions of these systems of diophantine equations don＇t exist.