The Collaborative International Dictionary of English v.0.48:

Require \Re*quire"\ (r?-kw?r"), v. t. [imp. & p. p. Required
   (-kw?rd"); p. pr. & vb. n. Requiring.] [OE. requeren,
   requiren, OF. requerre, F. requ?rir; L. pref. re- re- +
   quaerere to ask; cf. L. requirere. See Query, and cf.
   Request, Requisite.]
   1. To demand; to insist upon having; to claim as by right and
      authority; to exact; as, to require the surrender of
      property.
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            Shall I say to Caesar
            What you require of him?              --Shak.
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            By nature did what was by law required. --Dryden.
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   2. To demand or exact as indispensable; to need.
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            Just gave what life required, and gave no more.
                                                  --Goldsmith.
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            The two last [biographies] require to be
            particularly noticed.                 --J. A.
                                                  Symonds.
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   3. To ask as a favor; to request.
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            I was ashamed to require of the king a band of
            soldiers and horsemen to help us against the enemy
            in the way.                           --Ezra viii.
                                                  22.
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   Syn: To claim; exact; enjoin; prescribe; direct; order;
        demand; need.
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WordNet (r) 3.0 (2006):

required
    adj 1: necessary for relief or supply; "provided them with all
           things needful" [syn: needed, needful, required,
           requisite]
    2: required by rule; "in most schools physical education is
       compulsory"; "attendance is mandatory"; "required reading"
       [syn: compulsory, mandatory, required]

Moby Thesaurus II by Grady Ward, 1.0:

42 Moby Thesaurus words for "required":
   absolute, binding, called for, compulsatory, compulsory,
   conclusive, de rigueur, decisive, decretory, dictated, entailed,
   essential, final, hard-and-fast, imperative, imperious, imposed,
   indicated, indispensable, inevitable, involuntary, irreducible,
   irreductible, irreplaceable, irrevocable, mandated, mandatory,
   must, necessary, needed, needful, obligatory, peremptory,
   prerequisite, prescript, prescriptive, requisite, ultimate,
   unforgoable, vital, wanted, without appeal