Is it permissible for university students residing in a city other than their hometown to shorten prayers, knowing that they visit their hometown every week or two?

First: If you are in your hometown, you complete the prayer.

Second: If the distance between your city and the university city is a distance that permits shortening prayers (approximately 80 kilometers), then you shorten the prayer while traveling to it.

Third: Upon arriving at the university city:

If you intend to stay for more than four days, you complete the prayer from the moment you enter.

If you intend to stay for four days or less, or you are undecided about the duration, then you are considered a traveler and you shorten the four-rak'ah prayer to two rak'ahs, unless you pray behind a resident imam, in which case you complete it with him. You are required to attend the prayer with the mosque congregation.