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Natural numbers satisfying an inequality

Source: Ukrainian National Math Olympiad 4th round

October 20, 2014
inequalitiesnumber theory unsolvednumber theory

Problem Statement

It is known that for natural numbers a,b,c,da,b,c,d and nn the following inequalities hold: a+c<na+c<n and a/b+c/d<1a/b+c/d<1. Prove that a/b+c/d<1āˆ’1/n3a/b+c/d<1-1/n^3.
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