a student of a Saratov university

[englishhobby]

Student B. You are a British student who has come to Saratov on a student exchange program. You are talking to a student of a Saratov university about the system of transportation in your countries/cities.

Above is a situation for students to make up a dialogue (paired work). Is the indefinite article correctly used here (if we don't know which particular university the student is from)? Is the instruction as a whole correct?

 

[MikeNewYork]

Student B. You are a British student who has come to Saratov on a student exchange program. You are talking to a student of a Saratov university about the system of transportation in your countries/cities.

Above is a situation for students to make up a dialogue (paired work). Is the indefinite article correctly used here (if we don't know which particular university the student is from)? Is the instruction as a whole correct?

If there is more than one university in Saratov, "a" is correct.