Question 106
Prove or disprove that for every integer $n \ge 2009$ one can choose two distinct pairs of fractions from the sequence $\frac{1}{n}, \frac{2}{n-1}, \frac{3}{n-2}, \dots, \frac{n-1}{2}, \frac{n}{1}$ so that the sums of fractions in pairs are equal. (A. Shapovalov, K. Knop)