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Number theory again?

Source: Pan-American Girls' Mathematical Olympiad 2022, P5

October 30, 2022
PAGMOpositive integers

Problem Statement

Find all positive integers kk for which there exist aa, bb, and cc positive integers such that ∣(a−b)3+(b−c)3+(c−a)3∣=3⋅2k.\lvert (a-b)^3+(b-c)^3+(c-a)^3\rvert=3\cdot2^k.
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