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Unformatted text preview: z (mod m ). 4. Let a, b Z and m P . Suppose that S is the statement: If a 0 (mod m ) or b 0 (mod m ), then ab 0 (mod m ). (a) Write down the converse of S .  (b) Prove or disprove the converse of S .  5. Determine the complete solution to the linear congruence 46 x 14 (mod 270).  6. (a) Solve the system of congruences  x 22 (mod 27) x 11 (mod 31) (b) If d = gcd( m, n ) and the system of congruences  x a (mod m ) x b (mod n ) has a solution x = x , prove that d | a-b . 7. Suppose that a is an integer with a 7 1 (mod 7). Prove that a 7 1 (mod 7 2 ). ...
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This note was uploaded on 10/21/2010 for the course MATH 135 taught by Professor Andrewchilds during the Fall '08 term at Waterloo.
- Fall '08