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I have seen the following problem in my regular study, which I am not able to solve. Please solve it for me.

Let $C_0,..., C_{k-1}$ be fixed integers and consider the recurrence relation of order $k$, $X_{n+k} = C_{k-1} X_{n+k-1} + C_{k-2} X_{n+k-2} + \cdots + C_1 X_{n+1} + C_0 X_n$. Show that once $k$ values of $X_m$ are specified, all values of $X_n$ are determined.

Let $f(r) = r^k - C_{k-1} r^{k-1} - \cdots - C_0$; we call this characteristic equation (polynomial) of the recurrence relation. Show that if $f(p) = 0$ then $X_n = cp^n$ satisfies the recurrence relation for any $c$ belongs to $\mathbb{C}$ (complex member)

Thanks in very advance... mahima

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    Try working with small values of n, and then try induction for a general proof.2011-08-06
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    You have posted several low-quality questions without accepting any answers on them. In addition, "please solve it for me" is not really in the spirit of this site: you should be here to _learn_, not just to copy answers. Think about what you don't understand, and ask about that instead.2011-08-06
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    Please format more clearly using $\LaTeX$. Then please do not assign homework-the imperative mode is offensive. Can you see why if you have $k$ values you have the rest? Then plug in the suggestion and see what happens.2011-08-06

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