# Minimum 11 Multiples

**Number Theory**Level 5

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 \(11\)?