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Found problems: 1

2003 Gheorghe Vranceanu, 2
Tags: real analysis , cauchy sequence
Let $ a $ be a positive real number and $ \left( x_n\right)_{n\ge 1} $ be a sequence of pairwise distinct real numbers satisfying the properties: $ \text{(i) } x_n\in (0,a) , $ for any natural numbers $ n $ $ \text{(ii) } \left| x_n-x_m \right|\geqslant\frac{m+n}{amn} , $ for all pairs $ (m,n) $ of distinct natural numbers Show that $ a\geqslant 2. $