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B1

Part of 2011 Putnam

Problems(1)

Putnam 2011 B1

Source:

12/5/2011
Let hh and kk be positive integers. Prove that for every ε>0,\varepsilon >0, there are positive integers mm and nn such that ε<∣hm−kn∣<2ε.\varepsilon < \left|h\sqrt{m}-k\sqrt{n}\right|<2\varepsilon.
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