\[\ 4,\ 9,\ 36,\ 81,\ 100,\ 576,\ 625 , \ldots \]

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?

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