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Unformatted text preview: Z 103 . Express your answer in the form [ b ] 103 where 0 b < 103. (b) Solve the congruence equation 15 x 8 mod 103. Express your answer in the form [ b ] 103 where 0 b < 103. (c) Solve the system of simultaneous linear congruences: x 8 mod 103 x 3 mod 48 : 4. [20 Points] This problem concerns arithmetic modulo 21. All answers should be expressed in the form [ a ] 21 with a an integer satisfying 0 a < 21. (a) Compute [9] 21 + [16] 2 21 . (b) Compute [9] 21 [16] 21 + [3] 21 [14] 21 . (c) Compute [5] 1 21 . (d) List the invertible elements of Z 21 . (e) List the zero divisors of Z 21 . 5. [20 Points] (a) State Eulers Theorem precisely. Be sure to carefully state the requisite hypotheses. (b) Compute (200). As usual ( n ) denotes the Euler function applied to n . (c) Compute 7 177 mod 200. Math 4023 Section 1 February 11, 2009 1...
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 Fall '09

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