# Interpolation and Integers

Let $$a,b,c \in \mathbb{Z_4}$$ be interpolated by a quadratic polynomial $$f$$. That is, $$f(1) = a, f(2) = b$$ and $$f(3) =c$$. For how many triples of $$(a,b,c)$$ does $$f$$ have integer (including zero) coefficients?

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