ownership/permissions problem

I have Mac S X 10.5.4 (the latest) and Acrobat 6.0 (not nearly the
latest but the best that I can do for now).

Acrobat 6 won't startup without the admin password being supplied and
I've learned it's because a file that it writes to (Adobe Registration
Database) needs world-write access. Photoshop and Illustrator also
write to this file but only Acrobat appears to need world-write
access. What would be the best solution to this problem?

$ ls -ald /Library /Library/Application\ Support/ /Library/Application
\
Support/Adobe ./Adobe\ Registration\ Database
drwxrwxr-t+ 59 root admin 2006 Jul 17 15:16 /Library
drwxrwxr-x 22 root admin 748 Jul 17 11:15 /Library/Application
Support/
drwxrwxr-x 28 admin admin 952 Jul 17 20:20 /Library/Application
Support/Adobe
-rw-rw-rw- 1 root admin 672 Jul 17 20:20 ./Adobe Registration
Database

Many thanks.