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Algebra Level 5

Let p,qp,q and rr be the roots of the equation x3+3x=2x2+4x^3 +3x = 2x^2+4 , and denote Sn=pn+qn+rnS_n = p^n + q^n + r^n. Find the sum of all positive integers mm satisfying Sm=2|S_m| =2 .

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