How Can I get the computer to remember the administator's password when Im dowloading something?

I don't see why the computer you're on should constantly prompt you with the administrator's password unless you're on a non-administrator account and you aren't given privileges to download files of any sort.

If you're the owner of the computer, you'll need to log out of that account and log back onto the administrator account and use that instead. Otherwise, you should proceed as you are.

Hope this helps!