Are they all close to power s of 2?

Algebra Level 4

Let a,ba,b and cc be roots of P(x)=x3+3x2+4x8P(x) = x^3 + 3x^2 + 4x - 8. Suppose Sn=an+bn+cnS_n= a^n + b^n + c^n . If S3=2m+1S_3 = 2^m + 1 and S5=2n+1S_5 = 2^n + 1 , find the value of m+nm+n.

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