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perfect cube of an integer

Source: Bosnia and Herzegovina Team Selection Test 2005 problem 3 day 2

October 6, 2017
number theoryIntegersperfect cube

Problem Statement

Let aa, bb and cc are integers such that ab+bc+ca=3\frac{a}{b}+\frac{b}{c}+\frac{c}{a}=3. Prove that abcabc is a perfect cube of an integer.
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