M135F08A6

# M135F08A6 - MATH 135 Fall 2008 Assignment#6 Due Wednesday...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 135 Fall 2008 Assignment #6 Due: Wednesday 29 October 2008, 8:20 a.m. Hand-In Problems 1. In parts (a) to (d), state the answer. No justification is necessary. In parts (e) to (h), explain how you got your answer. (a) Is- 14 ≡ 22 (mod 18)? (b) Is 2473 ≡ - 26 (mod 17)? (c) Is 8 16 ≡ 4 (mod 12)? (d) For how many n ∈ P with 1 ≤ n ≤ 2008 is n ≡ 0 (mod 4)? (e) What is the remainder when 8 243 is divided by 3? (f) Is 8 24 + 13 12 divisible by 7? (g) Determine the remainder when 3 47 5 74 + (- 9) 10 is divided by 13. (h) For how many m ∈ P with m > 1 is 14 ≡ - 58 (mod m )? 2. Suppose that a,b ∈ Z and m ∈ P , with a ≡ b (mod m ). Prove by induction that a n ≡ b n (mod m ) for every n ∈ P . 3. Suppose that a,b ∈ Z and m,n ∈ P . Prove that an ≡ bn (mod mn ) if and only if a ≡ b (mod m ). 4. Suppose that p is a prime number with p > 3. (a) By consider the possible remainders when p is divided by 4, prove that p ≡ 1 or 3 (mod 4)....
View Full Document

## This note was uploaded on 09/04/2009 for the course MATH 135 taught by Professor Andrewchilds during the Fall '08 term at Waterloo.

### Page1 / 2

M135F08A6 - MATH 135 Fall 2008 Assignment#6 Due Wednesday...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online