hw27 - r,s so that ra + sn = 1.] Exercise 80. For n N , n...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Intro to Abstract Math Homework 27 Fall 2009 Due November 23 Exercise 78. For each pair ( a,b ), find gcd( a,b ) and express it in the form ra + sb with r,s Z . a. a = 11, b = 3 b. a = 42, b = 77 c. a = 420, b = 288 Exercise 79. Let n N , n 2 and let a Z n . Prove that if gcd( a,n ) = 1 then there is a b Z n so that a · n b = 1. [ Hint: If gcd( a,n ) = 1 then there are integers
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: r,s so that ra + sn = 1.] Exercise 80. For n N , n 2, let U ( n ) = { a Z n | gcd( a,n ) = 1 } . a. Use the result of the previous exercise to show that ( U ( n ) , n ) is a group. b. Determine whether or not U ( n ) is cyclic for n = 8 , 9 , 10 , 11 , 12....
View Full Document

This note was uploaded on 02/29/2012 for the course MATH 3326 taught by Professor Ryandaileda during the Fall '09 term at Trinity University.

Ask a homework question - tutors are online