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Dividing $\mathbb{Z}$ into triples with square

Source: Balkan-2010 Shortlist

August 16, 2018
number theory

Problem Statement

Determine whether it is possible to partition Z\mathbb{Z} into triples (a,b,c)(a,b,c) such that, for every triple, ∣a3b+b3c+c3a∣|a^3b + b^3c + c^3a| is perfect square.
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