For an arithmetic sequence $\{ a_n \} \in \mathbb{R}$, there exists a $p(x):p(r)=a_r$ for all $r$. Is the same true if $\{ a_n \} \in \mathbb{R}[i]$?

by heepo   Last Updated September 12, 2019 04:20 AM

For an arithmetic sequence $\{ a_n \} \in \mathbb{R}$ of degree $k$, there exists a degree-$k$ polynomial $p(x):p(r)=a_r$ for all $r \in \mathbb{Z}_0^+$. Is the same true if $\{ a_n \} \in \mathbb{R}[i]$, $i=\sqrt{-1}$? Is there an existing proof of this that I have failed to find? I would appreciate pointers to an existing proof and/or hints on how to begin my own.



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