I have three entities: students, professors and essay_topics.
Situation: students can write several essays with an essay_topic under supervision of a professor. (bold: entities)
But they can only write an essay under supervision of a specific professor once. (not two times the same professor) And they can not write an essay with the same essay_topic as they did.
That's the only restriction, but it should be possible that: A Professor can supervise several students with the same essay_topic. Different professors can supervise different student with the same essay_topic.
So we have a relationship essay(StudentID, EssayTopicID, ProfessorID). But I don't see what are the primary keys now. Or what kind of relationship do we have here? I would guess n:1:1 (er model). But then, only StudentID would be the primary key of that table – what's actually wrong, because the student only could write one essay…