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RSolve[{1 == b ((c k[t - 1]^a - k[t])/(c k[t]^a - k[t + 1])) c a k[t]^(a - 1), 
        k[1] == b, k[3] == a}, k[t], t]

I tried to read the documentation in Help and searched through Google. But I still can't make Mathematica to solve my recurrence function. I am new to Mathematica. Is there any place where I made mistakes? And is there any way that I can solve this function?

I'm using Mathematica 8.0.4 for Mac.

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What are the values of your various symbols? –  Mr.Wizard Jan 26 '13 at 5:53
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