Unformatted text preview: 1 } so there are d possiblities for r . Division Algorithm for Z Theorem. Division Algorithm for Z . (7 th edition, page 62) ( ∀ n ∈ Z ) ( ∀ d ∈ Z \ { } ) ( ∃ ! q ∈ Z ) ( ∃ ! r ∈ Z ) [ ( n = dq + r ) ∧ (0 ≤ r <  d  ) ] equivalently ( ∀ n ∈ Z ) ( ∀ d ∈ Z \ { } ) ( ∃ ! q ∈ Z ) ( ∃ ! r ∈ { , 1 , . . . , (  d  1) } ) [ n = dq + r ] Remark. Here: r ∈ { , 1 , 2 , . . . , (  d  1) } so there are d possiblities for r . 1...
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This note was uploaded on 12/13/2011 for the course MATH 300 taught by Professor Staff during the Fall '11 term at South Carolina.
 Fall '11
 Staff
 Advanced Math, Division

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