Let a, b be the fundamental solution of $\displaystyle x^2 - dy^2 =1$ and set $\displaystyle \epsilon = a+b \sqrt{d} $ How do I show that there exists a solution u, v of the negative Pell equation with $\displaystyle 1< u+v \sqrt{d} < \epsilon $?

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- Dec 8th 2009, 03:08 PMezongPell equations
Let a, b be the fundamental solution of $\displaystyle x^2 - dy^2 =1$ and set $\displaystyle \epsilon = a+b \sqrt{d} $ How do I show that there exists a solution u, v of the negative Pell equation with $\displaystyle 1< u+v \sqrt{d} < \epsilon $?