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## Homework Statement

Let f be a one-to-one function from X = {1,2,...n} onto X. Let f

^{ k }= f(f(f(...f(x))) be the k-fold composition of f with itself. Show that there are distinct positive integers i and j such that f

^{ i }(x) = f

^{ j }(x) for all x in X.

## Homework Equations

pigeonhole principle?

## The Attempt at a Solution

The section is on counting and the pigeonhole principle. But I'm not sure how to start this one.