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| 1/(a+25)- 1/(b+25)| < 1/100

Source: Netherlands - Dutch NMO 1974, year 1974-75 (also named as 1975 -1) p3

January 27, 2023
algebranumber theoryinequalities

Problem Statement

Proove that in every five positive numbers there is a pair, say a,ba,b, for which ∣1a+25−1b+25∣<1100.\left| \frac{1}{a+25}- \frac{1}{b+25}\right| <\frac{1}{100}.
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