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max No. of positive integers so for that any 2 of them a,b : |a - b| >=ab/100

Source: Mexican Mathematical Olympiad 2004 OMM P2

July 31, 2018
number theoryIntegersInequality

Problem Statement

Find the maximum number of positive integers such that any two of them a,ba, b (with a≠ba \ne b) satisfy that∣a−b∣≥ab100. |a - b| \ge \frac{ab}{100} .
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