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Given $P$, a polynomial of degree $n$, such that its values at $n+1$ points are $P(x) = r^x$ for $x = 0,1, \ldots, n$ and some real number $r$, I need to calculate $P(n+1)$?

Can this be done without Lagrange interpolation?

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    If $P(x) = r^x,$ then $P(n+1) = r^{n+1} = r^n r = P(n)P(1).$ Am I mis-reading the question?2012-07-17
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    @J.D. It seems that holds only for $x=1..n$, so we can't be sure about $n+1$.2012-07-17
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    He said $P(x)$ is a polynomial of degree $n$ with the specific values for $x=0,...,n$.2012-07-17

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