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Here you can find hints and tips if you are having issues getting the SDK installer to work.
Linux
Adobe no longer provide updates for their installer for the AIR runtime used by the installer, so clicking the installer badge may give an error, or the package it sends you will fail to correctly install. Workarounds to install the AIR runtime are listed here.
Ubuntu and other .deb based system (such as Debian)
For 32bit systems
sudo ln -s /usr/lib/i386-linux-gnu/libgnome-keyring.so.0 /usr/lib/libgnome-keyring.so.0
sudo ln -s /usr/lib/i386-linux-gnu/libgnome-keyring.so.0.2.0 /usr/lib/libgnome-keyring.so.0.2.0
For 64bit systems
sudo ln -s /usr/lib/x86_64-linux-gnu/libgnome-keyring.so.0 /usr/lib/libgnome-keyring.so.0
sudo ln -s /usr/lib/x86_64-linux-gnu/libgnome-keyring.so.0.2.0 /usr/lib/libgnome-keyring.so.0.2.0
Then for either system:
download the Adobe AIR installer by running the following command:
Once downloaded, you need to add "execute" permission to the installer:
sudo chmod +x AdobeAIRInstaller.bin
The last thing to do is executing the Adobe AIR installer:
sudo ./AdobeAIRInstaller.bin
Confirm is installed once complete
dpkg -l|grep adobeair
should list 'ii adobeair 1:2.6.0.19170 i386 Adobe AIR 2'. You can now click the installer on the main download page and it should work fine.
(thanks to http://www.ubuntubuzz.com/2012/08/how-to-install-adobe-air-on-ubuntu-1204.html)