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ab is a perfect cube if ab(a-b) divides a^3+b^3+ab

Source: Baltic Way 2007

November 30, 2010
geometrysearchfunctionnumber theorynumber theory proposed

Problem Statement

Let aa and bb be positive integers, b<ab<a, such that a3+b3+aba^3+b^3+ab is divisible by ab(aāˆ’b)ab(a-b). Prove that abab is a perfect cube.
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