M135W09A8 - a-b then this system has a unique solution...

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MATH 135 Winter 2009 Assignment #8 Due: Wednesday 18 March 2009, 8:20 a.m. Hand-In Problems 1. Solve the simultaneous congruences 3 x 11 (mod 25) 5 x 1 (mod 31) 2. Solve the simultaneous congruences x 2 (mod 5) x 7 (mod 11) x 9 (mod 13) 3. Suppose that a and b are integers not divisible by 3 or 7. Prove that a 6 b 6 (mod 21). 4. Use CRT to fnd the complete solution oF x 3 17 (mod 99). 5. Consider the system oF simultaneous congruences x a (mod m ) x b (mod n ) Prove that iF gcd(m,n) divides
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Unformatted text preview: a-b , then this system has a unique solution modulo mn gcd ( m, n ) . 6. Solve the system oF simultaneous congruences x ≡ 2 (mod 21) x ≡ 5 (mod 18) 7. ±ind all integer solutions to the Diophantine equation 5 x 2 + x-7 y + 6 = 0. Recommended Problems 1. Text, page 83, #50 2. Text, page 83, #52 3. Text, page 83, #55 4. Text, page 86, #81 5. Text, page 86, #84 6. Text, page 87, #95...
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