# Show that there exist a positive integer $M>1$

Let $f$ be a bijective (one-one and onto) function from the set $$A=\{1,2,3,…,n\}$$ to itself. Show that there is a positive integer $M>1$ such that $$f^M(i)=f(i)$$ for each $i\in A$

[$f^M$ denotes the composite function $f\times f \times f \times \dotsb \times f$, repeated $M$ times.]