  This note is an attempt to attack a conjecture of Fraenkel and Simpson stated
in 1998 concerning the number of distinct squares in a finite word. By counting
the number of (right-)special factors, we give an upper bound of the number of
{\em $k$-powers} in a finite word for any integer $k\geq 3$. By {\em
$k$-power}, we mean a word of the form $\underbrace{uu...u}_{k \;
\text{times}}$.

Combinatorics