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The smallest positive value

Source: India National Olympiad 2002, Problem 2

October 10, 2005
number theory solvednumber theory

Problem Statement

Find the smallest positive value taken by a3+b3+c3āˆ’3abca^3 + b^3 + c^3 - 3abc for positive integers aa, bb, cc . Find all aa, bb, cc which give the smallest value