Installing Flash Player

Unable to install Abobe Flash Player in Parallels Desktop 7 and XP Pro on my two mac machines.

One is iMac running Leopard; MacBook Pro running Lion. All latest updates.

When I download the Flash player from the Adobe website, I keep getting a windows error message that the download is not a valid 32 bit application.

What am I missing? Do I have to download a Mac or other special version?

Thanks in advance...