Indeed.
I do not understand how do I synchronize btc core apart from executing bitcoin-qt, which downloads blocks until it stops and looks synchronized.
That's all you need to do. When you open Core, you should not see any out-of-sync overlay or a green bar at the bottom. If you hover over the checkmark at the bottom right hand corner, it will tell you how many blocks it has synced. Compare that to a block explorer to check if you are in sync.
If Core is in sync, then Armory somehow got off sync. With Core running, start Armory. Go to Help > Rebuild and Rescan Databases and click Yes. Then restart Armory. This should fix your problems.