MathDB
Differences of fractions

Source: 239 2019 S1

July 31, 2020

Problem Statement

The following fractions are written on the board 1n,2n−1,3n−2,…,n1\frac{1}{n}, \frac{2}{n-1}, \frac{3}{n-2}, \ldots , \frac{n}{1} where nn is a natural number. Vasya calculated the differences of the neighboring fractions in this row and found among them 1000010000 fractions of type 1k\frac{1}{k} (with natural kk). Prove that he can find even 50005000 more of such these differences.
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