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Mock AIME 3 Pre 2005 Problems/Problem 4

Revision as of 22:03, 24 February 2007 by Me@home (talk | contribs)
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$4.$ $\zeta_1, \zeta_2,$ and $\zeta_3$ are complex numbers such that

$\zeta_1 + \zeta_2 + \zeta_3 = 1$

$\zeta_1^{2} + \zeta_2^{2} + \zeta_3^{2} = 3$

$\zeta_1^{3} + \zeta_2^{3} + \zeta_3^{3} = 7$


Compute $\zeta_1^{7} + \zeta_2^{7} + \zeta_3^{7}$.

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