Whose sum is this?

Algebra Level 4

Let \(a, b,c\) and \(d\) be the roots of the equation \(x^4 + 4x^3 + 4x^2 + 4x + 4 = 0 \). And denote \(S_n =a^n + b^n + c^n + d^n\). What is the smallest positive integer \(m\) such that \(S_m, S_{m+1}, S_{m+2} , S_{m+3} , \ldots \) are all divisible by 8?

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