Dirichlet's approximation theorem: Difference between revisions

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==Simultaneous version==

The simultaneous version of the Dirichlet's approximation theorem states that given real numbers <math>\alpha_1, \ldots, \alpha_d</math> and a natural number <math>N</math> then there are integers <math>p_1, \ldots, p_d, q\in\Z,1\le q\leq N^d</math> such that <math>\left|\alpha_i-\frac{p_i}q \right| \le \frac1{qN^{1/d}}.</math><ref>Schmidt, p. 27 Theorem 1B</ref>

==Method of proof==