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Easy Algebra

Source: Taiwan 1st TST 2005, 1st independent study, problem 2

August 12, 2005
algebra solvedalgebra

Problem Statement

Does there exist an positive integer nn, so that for any positive integer m<1002m<1002, there exists an integer kk so that m1002<kn<m+11003\displaystyle \frac{m}{1002} < \frac{k}{n} < \frac {m+1}{1003} holds? If nn does not exist, prove it; if nn exists, determine the minimum value of it. I know this problem was easy, but it still appeared on our TST, and so I posted it here.
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