hw4 - n below. (a) n = 5 182 , m = 77. (b) n = 3 1000000 ,...

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Math 465 Problem Set 4 Due Friday, February 15, 2008 1. Solve the simultaneous congruences x 3 (mod 6) , x 5 (mod 35) , x 7 (mod 143) . 2. Prove that x b 1 (mod m 1 ) x b 2 (mod m 2 ) is solvable if and only if ( m 1 , m 2 ) | b 1 - b 2 . In this case, prove that the solution is unique modulo [ m 1 , m 2 ]. 3. Using Euler’s Theorem, find the least nonnegative residue modulo m of each integer
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Unformatted text preview: n below. (a) n = 5 182 , m = 77. (b) n = 3 1000000 , m = 14. 4. Use Euler’s theorem to find all incongruent solutions of each congruence below: (a) 3 x ≡ 1 (mod 5). (b) 10 x ≡ 15 (mod 55). 5. Let p and q be distinct prime numbers. Prove that p q-1 + q p-1 ≡ 1 (mod pq ). 1...
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This note was uploaded on 07/23/2008 for the course MATH 465 taught by Professor Yee during the Spring '08 term at Pennsylvania State University, University Park.

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