Unformatted text preview: (b) Use your work from part (a) to write the greatest common divisor as a linear combination of 22 and 291. (c) Solve the equation 291 x = 5 in Z 22 . 3. Let p be an integer other than 0, ± 1 with this property: For all integers b and c , if p | bc , then p | b or p | c . Prove that p is prime. 4. Prove: For all integers a and b and all positive integers n , a ≡ b (mod n ) if and only if a and b have the same remainder when divided by n . 5. Let a and n be integers with n > 1. Prove: If ( a, n ) = 1 in Z , then the equation [ a ] ⊙ x =  has a solution in Z n . (This is the result of Corollary 2.10. You should not refer to that corollary in your proof.)...
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- Spring '03
- Algebra, Natural number, Greatest common divisor, positive integers, blue book