My flash drive is out of date and I’m being asked to download a new version.  It keeps asking me for my administrator user name and password, but we never installed one on this computer.  What do I do?  Again, it’s a MAC.  
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I think you are referring to Adobe Flash and not a flash drive. And yes, the computer asks for your username and password when installing an updated version of flash. Every computer has at least a username. That is most likely automatically populated when the prompt appears during an install. However, the password is not. This is part of the reason Macs are very secure. In order for anything to install, your username and password are required. Now, if a password was never assigned then you can try leaving the password field blank and just hit enter. If a password was created then you may have created a password hint. If a hint was created then that hint will appear after you’ve tried to enter a password 3 times. Hope that helps.