\documentstyle{letter}
\begin{document}
\address{3 Ames St. \\ Cambridge, MA 02139}
\signature{Kevin Iga \\ Student, MIT}
\begin{letter}
{The Mathematical Association of America\\
1529 Eighteenth St., N.\ W.\\
Washington, DC 20036}

\opening{Dear Sirs:}

I have been working on a problem for some time now, but I cannot find
any indication that anyone else had ever worked on it, which is
surprising to me, since I considered it a natural question.  I would
like to submit a query, since I have found some interesting
discoveries about the problem, and was wondering if anyone else has
worked on the subject, and if the same discoveries were already made.

The problem is this: given a continuous function $g(x)$, find all continuous
functions $f(x)$ such that $f(f(x))=g(x)$.

Other problems can be generated if the word, "continuous" is replaced
by "differentiable", "analytic", etc., or if $g(x)$ is a map from some
other space $X$ to itself (instead of $\Re$), or if we ask for a
function $f(x)$ such that $f(f(f(x))) = g(x)$.

I have completely solved the problem for continuous/differentiable
solutions for g(x) monotonic, and have developed a method for dealing with
some non-monotonic g(x).  In addition, if g(x) intersects the line y=x, I
can also find an analytic solution, and in some cases, can show that this is
unique.  I am also working on generalizing this into other spaces and taking
"one-third composites".

I would appreciate it if you could write to me concerning any previous work
on the subject.  Thank you.

\closing{Sincerely,}
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