# Are they all close to power s of 2?

Algebra Level 3

Let $$a,b$$ and $$c$$ be roots of $$P(x) = x^3 + 3x^2 + 4x - 8$$. Suppose $$S_n= a^n + b^n + c^n$$. If $$S_3 = 2^m + 1$$ and $$S_5 = 2^n + 1$$, find the value of $$m+n$$.

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