Requirement, requisite, prerequisite can all mean something that is regarded as necessary to the success or perfection of a thing.
Although requirement, the more general term, may be employed in place of requisite, it is the customary term when the idea to be conveyed is of something more or less arbitrarily demanded or expected, especially by those who lay down conditions (as for admission to college, for enlistment in the army or navy, for membership in a church, or for entrance into a course).
Requisite is the customary term when the stress is on the idea of something that is indispensable to the end in view, or is necessitated by a thing’s nature or essence or is otherwise essential and not arbitrarily demanded.
Prerequisite differs from requisite only in a stress on the time when something becomes indispensable; it applies specifically to things which must be known, or accomplished, or acquired as preliminaries (as to the study of a subject, the doing of a kind of work, or the attainment of an end).