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This error means that you have entered the wrong Download ID. Please log in to our site and follow the instructions on the Admin Tools Download ID page (found under the My, My Instructions menu item at the top menu of our site). Please do follow all of the instructions, even if you think they are unnecessary – I'd say especially if you think they are unnecessary.

Please note that you MAY have to go to Extensions, Manage, Update and click on the Clear Cache button before trying to update again. This is due to the way Joomla! caches update URLs under the hood. In some cases you might end up with the wrong download URL being used by Joomla even though you just entered or updated your Download ID. Clearing the updates cache works a treat in these cases.

I have confirmed that this is a side effect of how Joomla itself works, per my explanation above. I was able to trigger this behavior by installing AT 4.0.1 on a new Joomla! 3.6.4 site, entering my Download ID and then trying to update. I can also reproduce this on Joomla! 3.6.2 therefore the Joomla! version is irrelevant to your issue, as I explained. In fact, I can tell you that this code was first added sometime around Joomla! 2.5.3 because Joomla! had the bad habit of bringing down update servers since it was polling for updates all the time, effectively doing a distributed denial of service attack to developers' sites :)

In any case, you will need to press Clear Cache followed by Find Updates twice to let Joomla finally use the correct Download ID in its URL. If all else fails just wait 6* hours for the Joomla update cache to clear and then retry the update.

* 6 hours is the default setting. If you have modified it in the Options of the Extension Manager component that ships with Joomla you will have to wait as many hours as you've set there.