# Question 16

Algebra Level 5

$\large ( a + b\omega + c\omega^{2})^{3} +(a + c\omega + b\omega^{2})^{3}=0$

If $$a,b$$ and $$c$$ are distinct integers in a geometric progression which satisfy the equation above where $$\omega$$ is a non-real cube root of unity, what is the least possible value of $$|a| + |b| + |c|$$?

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