Rashi on Deuteronomy 6:9/רש"י על דברים ו׳:ט׳

1מזזות ביתך THE DOORPOSTS OF THY HOUSE — The word is written מזזת, to indicate that it is necessary to fix only one מזוזה to a door (cf. Menachot 34a).

2ובשעריך AND UPON THY GATES — the plural is used to include also the gates of courts and the gates of provinces and the gates of cities [in the requirement of mezuzah] (Yoma 11a).