# Minimum 11 Multiples

The polynomial $$f(x) = ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx^1 + g$$ has non-zero integral coefficients, and $$f(n)$$ is a multiple of $$11$$ whenever $$n$$ is an integer. What is the minimum number of coefficients: $$a, b, c, d, e, f, g$$, that must be a multiple of $$11$$?

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