Talk:Dirichlet's approximation theorem

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Mathematics rating:	Stub Class	Low Priority	Field: Number theory
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Geometry guy 15:45, 10 June 2007 (UTC)

Hi, I'm a new member and i'm interested in the following closely related problem. Suppose you are given a real number a and a bound c > 0. What does the set of all natural (or integral) numbers m satisfying for some integer b 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 [i₁,i₂]? Would be great if anybody could help! Thanks in advance!