Обсуждение:Теорема Дирихле о диофантовых приближениях

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Privet vsem! Prostite sa translit i otsutsvie snania russkoi matematicheskoi terminologii.

I am interested in the following closely related problem. Suppose you are given a real number $\alpha$ and a bound $c>0$. What does the set of all natural (or integral) numbers $q$ satisfying $\vert q\cdot \alpha -a\vert \leq c$ for some integer $a$ look like? Has this set any structure makes it easy to deal with it? Does anybody know if there are any good upper or lower bounds for the cardinality of the intersection of this set with a fixed interval $[i_{1},i_{2}]$?

Kazhdomu otvetu (konechno i na russkom) budu rad! Spasibo sa vnimanie!

Обсуждение не место для консультаций по математике. --Тоша 18:17, 10 сентября 2006 (UTC)

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