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Unformatted text preview: d ). *Hint for the hint: You know certain things are linear combinations of a and b . Can a small positive number be a linear combination of a and b ? 2. Prove that if p > 3 is prime, then 24  p 21. 3. If n Z and 5n , show that n 2 k (mod 5) for some integer k . 4. Find a + b (mod n ), ab (mod n ), and ( a + b ) 2 (mod n ) if a = 4003, b =127, and n = 85. 5. Find all integers 0 x < n satisfying each of the following congruences. (i) 3 x 4 (mod 6) (ii) 4 x 2 (mod 6) (iii) 4 x 3 (mod 7) (iv) 4 x 3 (mod 6) (v) 2 x 18 (mod 50) 1...
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This note was uploaded on 12/07/2011 for the course MATH 210 taught by Professor Staff during the Spring '08 term at University of Delaware.
 Spring '08
 Staff
 Integers

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