Unformatted text preview: Z b a ∈ , and P m ∈ with m > 1. (a) (1 mark) Give the definition of the statement “ ( ) m b a mod ≡ ”. (b) (4 marks) Prove that if a and b have the same remainder when divided by m , then ( ) m b a mod ≡ . 4. (8 marks) Solve the simultaneous congruencies ( ) ( ) 64 mod 59 81 mod 32 ≡ ≡ x x 5. (3 marks) Consider the statement “For all Z c b a ∈ , , , if a  bx + cy for all integers x and y , then a  b and a  c .” Is this statement TRUE or FALSE? Prove your answer. 6. (6 marks) Suppose that p , q and r are prime numbers and that p is odd. If p  2 q + r and p  2 q – r , prove that q = r ....
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 Fall '08
 ANDREWCHILDS
 Division, Remainder, Prime number, Divisor

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