Hi Hugo,
I understand you encountered the error message “An unknown error has occurred, the error code is: 805240834” during the activation of Outlook for Mac.
To fix this issue, there is an article providing the workaround, please refer to it via
http://community.office365.com/en-us/w/exchange/5867.outlook-for-mac-devices-known-issues.aspx.
Please let us know if it can be fixed.
Thanks,
Eric Yang