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x_m / y_m <= B x_n / y_n

Source: Polish MO Finals 1979 p4

August 24, 2024
algebrainequalities

Problem Statement

Let A>1A > 1 and B>1B > 1 be real numbers and (xn) be a sequence of numbers in the interval [1,AB][1,AB]. Prove that there exists a sequence (yn)(y_n) of numbers in the interval [1,A][1,A] such that xmxn≤Bymyn   for   all   m,n=1,2,...\frac{x_m}{x_n}\le B\frac{y_m}{y_n} \,\,\, for \,\,\, all \,\,\, m,n = 1,2,...
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