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That is, suppose that I am at item n and I want to make a reference to item n - 3 without explicitly specifying it.

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\label item n-3 and \ref it. Probably you should clarify better your question. – egreg Mar 4 '13 at 22:01
up vote 5 down vote accepted

How about

    \item \number\numexpr\value{enumi}-3\relax

Here's a complete MWE:

\documentclass{article}

\begin{document}

\begin{enumerate}
    \item cow
    \item lion
    \item moo
    \item \number\numexpr\value{enumi}-3\relax
    \item meow
\end{enumerate}
\end{document}
share|improve this answer
    
Do you need \relax after the calculation? – azetina Mar 5 '13 at 0:07
    
@azetina probably a good idea, thanks – cmhughes Mar 5 '13 at 2:11

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