Not quite so simple, but makes things certainly easier.
"As an EU citizen, you have the right to move to any EU country to live, work, study, look for a job or retire.
You can stay in another EU country for up to 3 months without registering there but you may need to report your presence. The only requirement is to hold a valid national identity card or passport. If you want to stay longer than 3 months, you may need to register your residence.
In many EU countries, you need to carry an identity card or passport with you at all times. In these countries, you could be fined or temporarily detained if you leave your identity documents at home - but you cannot be forced to return to your home country for this reason alone. "