PART I Let a = 40. What is a mod n? Let b 6. What is b mod n? Let c = 37. What is c mod n? Let d = 32. What is d mod n? Let e 38. What is e mod n?

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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Could you give me the answers of the four questions,please.Thanks

PART I
Let a 40. What is a mod n?
Let b
6. What is b mod n?
Let c =37. What is c mod n?
Let d 32. What is d mod n?
Let e 38. What is e mod n?
=
PART II
Fill in the following multiplication table mod 7:
aa mod 7 =
ca mod 7 =
ea mod 7
=
ac mod 7 =
cc mod 7 =
ec mod 7 =
ae mod 7 =
ce mod 7 =
ee mod 7 =
000
Transcribed Image Text:PART I Let a 40. What is a mod n? Let b 6. What is b mod n? Let c =37. What is c mod n? Let d 32. What is d mod n? Let e 38. What is e mod n? = PART II Fill in the following multiplication table mod 7: aa mod 7 = ca mod 7 = ea mod 7 = ac mod 7 = cc mod 7 = ec mod 7 = ae mod 7 = ce mod 7 = ee mod 7 = 000
PART III
Using your results in Part I, fill in the following multiplication table mod 7:
(a mod 7 )(c mod 7 ) mod 7 =
(a mod 7 )(a mod 7 ) mod 7
=
=
(c mod 7 )(a mod 7 ) mod 7
=
(e mod 7 )(a mod 7 ) mod 7 =
=
(c mod 7 )(c mod 7 ) mod 7
=
(e mod 7 )(c mod 7 ) mod 7 =
(a mod 7 )(e mod 7 ) mod 7
(c mod 7 )(e mod 7 ) mod 7 =
(e mod 7 )(e mod 7 ) mod 7
PART IV
Consider your answers from Parts II and III. Can you make a conjecture relating them? Write it in the box below.
Transcribed Image Text:PART III Using your results in Part I, fill in the following multiplication table mod 7: (a mod 7 )(c mod 7 ) mod 7 = (a mod 7 )(a mod 7 ) mod 7 = = (c mod 7 )(a mod 7 ) mod 7 = (e mod 7 )(a mod 7 ) mod 7 = = (c mod 7 )(c mod 7 ) mod 7 = (e mod 7 )(c mod 7 ) mod 7 = (a mod 7 )(e mod 7 ) mod 7 (c mod 7 )(e mod 7 ) mod 7 = (e mod 7 )(e mod 7 ) mod 7 PART IV Consider your answers from Parts II and III. Can you make a conjecture relating them? Write it in the box below.
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