# Perfect Square's Factors Aren't Perfect?

$\ 4,\ 9,\ 36,\ 81,\ 100,\ 576,\ 625 , \ldots$

I have some perfect squares and I observe that each perfect square has an odd number of distinct factors. For example: $\begin{array} {} d(4)= 3, & d(36) =9, & d(81) = 5\end{array}$

Is it true that a perfect square always has an odd number of distinct factors?

×