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TOT 251 1990 Spring A J5 no (m, n) <= 1000 m/(n+1)< \sqrt2 < (m+1)/n

Source:

March 12, 2021
combinatoricsnumber theoryinequalities

Problem Statement

Find the number of pairs (m,n)(m, n) of positive integers, both of which are ≤1000\le 1000, such that mn+1<2<m+1n\frac{m}{n+1}< \sqrt2 < \frac{m+1}{n}
(recalling that 2=1.414213.. \sqrt2 = 1.414213...).
(D. Fomin, Leningrad)
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