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Math Help - Induction

  1. #1
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    Induction

    If x^{3}=x+1, prove, by induction or otherwise, that x^{3n}=anx+bn+cn x^{-1}, where a1=1, b1=1, c1=0, and an=an-1+bn-1, bn=an-1+bn-1+cn-1, cn=an-1+cn-1, for n=2,3,... .

    I have got nowhere with this. I am trying to use induction. Is there a typing mistake in the question.
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  2. #2
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    Re: Induction

    Quote Originally Posted by Stuck Man View Post
    Is there a typing mistake in the question.
    You can answer this if you calculate a_2, b_2 and c_2 and compare x^6 with a_2x+b_2+c_2.

    I think the claim should say x^{3n}=a_nx^2+b_nx+c_n where a_1=0 and b_1=c_1=1. The recurrence equations seem correct.
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  3. #3
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    Re: Induction

    I had done exactly that. Thanks for your suggestion. I will try it.
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