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?

Your answer seems reasonable.
Find out if you're right!