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Regional Olympiad - FBH 2016 Grade 9 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2016

September 22, 2018
number theorydivisible

Problem Statement

Let aa and bb be distinct positive integers, bigger that 10610^6, such that (a+b)3(a+b)^3 is divisible with abab. Prove that ∣a−b∣>104 \mid a-b \mid > 10^4
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