Whose sum is this?

Algebra Level 5

Let a,b,ca, b,c and dd be the roots of the equation x4+4x3+4x2+4x+4=0x^4 + 4x^3 + 4x^2 + 4x + 4 = 0 . And denote Sn=an+bn+cn+dnS_n =a^n + b^n + c^n + d^n. What is the smallest positive integer mm such that Sm,Sm+1,Sm+2,Sm+3,S_m, S_{m+1}, S_{m+2} , S_{m+3} , \ldots are all divisible by 8?

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