Mock AIME 3 Pre 2005 Problems/Problem 4: Difference between revisions

Revision as of 07:34, 14 February 2008

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

This problem needs a solution. If you have a solution for it, please help us out by adding it.

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+==Problem==
-<math>4.</math> <math>\zeta_1, \zeta_2,</math> and <math>\zeta_3</math> are complex numbers such that
+<math>\zeta_1, \zeta_2,</math> and <math>\zeta_3</math> are complex numbers such that
 <math>\zeta_1 + \zeta_2 + \zeta_3 = 1</math>
@@ Line 10: / Line 10: @@
 Compute <math>\zeta_1^{7} + \zeta_2^{7} + \zeta_3^{7}</math>.
+==Solution==
+{{solution}}
+==See also==