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Korea 1995

Source: Korea 1995

December 2, 2015
combinatoricspigeonhole principleKorea 1995

Problem Statement

For any positive integer mm,show that there exist integers a,ba,b satisfying ∣a∣≤m\left | a \right |\leq m, ∣b∣≤m \left | b \right |\leq m, 0<a+b2≤1+2m+20< a+b\sqrt{2}\leq \frac{1+\sqrt{2}}{m+2}
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