SYllabus when writing up your submission! the Homework Guidelines in the I. Complete the following exercises from Chapter 4: 4, 6, 7, 15, 16 II. Answer the following questions. 1. Make two copies of the following table. On one, show the results of addition modulo 7 (+ (mod 7); i.e. replace * with +), and on the other, show the results of multiplication modulo 7 (x (mod 7); i.e. replace * with x). 1 3 4. 1 2 3 4 6. (mod 7) (mod 7) 1 1 3. 3 4 4 6. 6. Why does this table represent all possible sums and products under addition and multipli- cation modulo 7? Hint: Think about the remainder classes for modulo 7 arithmetic. 2. Calculate (13, 000 + 2)10 (mod 13). 3. Find the remainder of 3456 when divided by the following. Hìnt: Use the 2.
SYllabus when writing up your submission! the Homework Guidelines in the I. Complete the following exercises from Chapter 4: 4, 6, 7, 15, 16 II. Answer the following questions. 1. Make two copies of the following table. On one, show the results of addition modulo 7 (+ (mod 7); i.e. replace * with +), and on the other, show the results of multiplication modulo 7 (x (mod 7); i.e. replace * with x). 1 3 4. 1 2 3 4 6. (mod 7) (mod 7) 1 1 3. 3 4 4 6. 6. Why does this table represent all possible sums and products under addition and multipli- cation modulo 7? Hint: Think about the remainder classes for modulo 7 arithmetic. 2. Calculate (13, 000 + 2)10 (mod 13). 3. Find the remainder of 3456 when divided by the following. Hìnt: Use the 2.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 18E
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Transcribed Image Text:SYllabus when writing up your submission!
the Homework Guidelines in the
I.
Complete the following exercises from Chapter 4:
4, 6, 7, 15, 16
II. Answer the following questions.
1.
Make two copies of the following table. On one, show the results of addition
modulo 7 (+ (mod 7); i.e. replace * with +), and on the other, show the results of
multiplication modulo 7 (x (mod 7); i.e. replace * with x).
1
3
4.
1
2
3
4
6.
(mod 7)
(mod 7)
1
1
3.
3
4
4
6.
6.
Why does this table represent all possible sums and products under addition and multipli-
cation modulo 7? Hint: Think about the remainder classes for modulo 7 arithmetic.
2.
Calculate (13, 000 + 2)10 (mod 13).
3.
Find the remainder of 3456 when divided by the following. Hìnt: Use the
2.
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