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  • Then we may find an integer $\rho$ such that $\left|\sqrt{\sigma} - \rho\right|_p < 1$, but there is a problem: if we write $\sqrt{\sigma} = \rho + \frac{1}{1/(\sqrt{\sigma} - \rho)}$, we have $\left|\frac{1}{\sqrt{\sigma} - \rho}\right|_p > 1$.
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