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User story is one of the popular way of writing requirement in Agile. Lot of Agilists prefer the User Story format. However, that is not the only way of writing requirements in Agile projects. You could write requirements in many ways, for e.g.Use Cases, Business Requirement Specification, BDD etc
Scrum is a framework. That means, Scrum describes the boundries and some minimal things that you need to do to create a product. What Scrum says is that you need to write requirements in a Product Backlog. Now Scrum does not tell you whether you write using User Story or a Use case or a BDD format. All that Scrum requires is that requirements be written.
Thus Scrum is non-prescriptive about writing requirements in a specific format. However, User Story still remains a very popular way of writing requirement in Scrum.