Interesting condition on three real numbers

Algebra Level pending

Choose the option which truthfully completes the following statement.

Let \(a,b,c \in \mathbb{R}\) such that \(|a|, |b|, |c| \neq 1\). Then \(\exists p,q,r \neq 0\) such that \(a = \dfrac{q-r}{p}, b = \dfrac{r-p}{q}, c = \dfrac{p - q}{r}\) if and only if...

\(A : a^3 + b^3 + c^3 = 3abc\)

\(B : ab + bc + ca = abc\)

\(C : a + b + c = -abc\)

\(D : ab + bc + ca = 0\)

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