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Divisibility inequality

Source: 2019 MEMO Problem T-7

August 30, 2019
number theoryinequalitiesMEMO 2019memo

Problem Statement

Let a,ba,b and cc be positive integers satisfying a<b<c<a+ba<b<c<a+b. Prove that c(a−1)+bc(a-1)+b does not divide c(b−1)+ac(b-1)+a.
Proposed by Dominik Burek, Poland
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