4023f11ex1a

# 4023f11ex1a - Name: Solutions Exam 1 Instructions. Answer...

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: Name: Solutions Exam 1 Instructions. Answer each of the questions on your own paper, and be sure to show your work so that partial credit can be adequately assessed. Put your name on each page of your paper. 1. [ 12 Points] (a) List all of the elements in Z / 24 . I Solution. Z / 24 = f 1 ; 5 ; 7 ; 11 ; 13 ; 17 ; 19 ; 23 g . J (b) How many elements are in the group Z / 1080 ? I Solution. j Z / 1080 j = (1080) = (2 3 3 3 5 = (2 3 ) (3 3 ) (5) = (2 3 2 2 )(3 3 3 2 )(5 1) = 4 18 4 = 288 : J (c) How many elements are in the group Z 12 Z 8 ? I Solution. j Z 12 Z 8 j = j Z 12 j j Z 8 j = 12 8 = 96. J 2. [16 Points] (a) Use the Euclidean algorithm to compute d = gcd(318 ; 714). (b) Find integers s and t so that d = 318 s + 714 t . I Solution. Use the matrix method for the Euclidean algorithm: 1 0 318 0 1 714 714 2 318=78 ! 1 318 2 1 78 318 4 78=6 ! 9 4 6 2 1 78 78 13 6=0 !...
View Full Document

## 4023f11ex1a - Name: Solutions Exam 1 Instructions. Answer...

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

View Full Document
Ask a homework question - tutors are online