There are only 2 ways that you can put a 2B tiller on a 582 with an aluminum rear.
1.) The way Cub Cadet offered: Use a Cat 0 3pt hitch and a special adapter that is rare as hens teeth to find.
----OR-----
2.) Build your own adapter and make the tiller work with a sleeve hitch.
I did #2.
http://www.onlycubcadets.net/forum/s...ad.php?t=23922
I have since moved my "adapter" to my 1050 and use it. Same set up as your 582.
You will need either a sleeve hitch, or cat 0 3pt to attach the tiller. If your tractor has neither, then you will have to get one or the other. Oh.... and you are going to want a spring assist too. That tiller is a heavy SOB, lol.