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Let $x,y,z$ be complex numbers such that

$$x+y+z = x^{5}+y^{5}+z^{5} = 0, \hspace{10pt} x^3+y^3+z^3=2$$

Find all possible values of

$$x^{2007}+y^{2007}+z^{2007}$$

  • 0
    I remember seeing this question and therefore did not see the missed $x^3+y^3+z^3=2$ and assumed it$2012-03-11
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    I get $2^{669}/3^{668}$.2012-03-11
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    @Kirthi: Where did you see this question?2012-03-11
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    I think it was one of questions several years back in usamts.org (competition for high school math)2012-03-11

2 Answers 2