# 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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