This preview shows page 1. Sign up to view the full content.
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 ....
View Full Document
This note was uploaded on 10/21/2010 for the course MATH 135 taught by Professor Andrewchilds during the Fall '08 term at Waterloo.
- Fall '08