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You have to reset the password. If you are using Mac OS X Snow Leopard or Leopard, see "Resetting your original administrator account password" > http://support.apple.com/kb/HT1274
If you are using OS X Lion or Mountain Lion (I'm sure that you are using Lion or Mountain Lion), see > http://discussions.apple.com/docs/DOC-4101
To install Adobe Flash or any other application you neeed to enter an administrator's name and password.
If you do not remember the original administrator name and password you can reset it.
OS X 10.7 Lion /10.8 Mountain Lion
Follow the instructions in the first and the third boxes.