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original poster
hbghlyj
posted 2022-6-9 03:24
Ivan Niven, Diophantine Approximation (Theorem 3.1, page 23)
Given an irrational number $\alpha$ there is an increasing sequence of positive integers: ${k_1}<{k_2}<\cdots$ such that for $i\geq1$, $$\{{{\alpha}k_i}\} < {\frac{1}{k_{i+1}}}$$ |
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