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Given two real numbers a and b and a threshold t>0, try to find the smallest positive integer n s.t. an and bn are both close enough to some integers with their difference less than t.

I think n does not always exist. But even if there does(in big t case), a fine algorithm for n is hard to develop.

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    I am not sure I fully understand the question. What do you mean by "$an$ and $bn$ are close enough to some integers"? Specifically, what is close enough? Whose difference is less than $t$, $an$ and $bn$, or the integers they are close enough to?2012-02-27

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