Modular Arithmetic: prime multiplication table

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Daniel Mansfield

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Name	Status	Author	Last Modified
Modular Arithmetic: prime multiplication table	Ready to use	Daniel Mansfield	26/05/2020 08:48
Modular Arithmetic: composite multiplication table	Ready to use	Daniel Mansfield	26/05/2020 08:46

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Question statement

Multiplication in modular arithmetic looks different to regular multiplication. Here is an example for multiplication in modulo $\var{p}$ .

{table(p)}

Use this multiplication table to answer following questions.

Give any introductory information the student needs.

			Name	Type	Generated Value

p	integer	13
a	integer	4
x1	integer	5
b	integer	12
x3	integer	3
x2	integer	8
inversea	number	10

Automatically regenerate variables?

Name

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Value

xxxxxxxxxx
 
random(5,7,11,13)

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Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

→ Used by:

a
b
inversea
x1
x2
x3

Statement
Variable testing condition
"Part a)" - prompt
"Part b)" - prompt
"Part c)" - prompt
"Part d)" - prompt

Advice

This question introduces the concept of multiplication in modular arithmetic. All the answers can be found by looking up the appropriate row and column in the given multiplication table.

Aside: It is easy to find the inverse of $a$ when working in $\mathbb Z_p$ for some prime number $p$ . By Fermat's Little Theorem $a^p \equiv a \pmod{p}$ , so if $a$ is not a multiple of $p$ then $a^{-1} \equiv a^{p-2} \pmod{p}$ .

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This question is used in the following exams:

Week 3: Modular arithmetic and relations by Daniel Mansfield in Discrete Mathematics.
CMPU1018 Assessment (2020-2021) by Blathnaid Sheridan in Blathnaid's workspace.
CMPU CA (2021-2022) by Blathnaid Sheridan in Blathnaid's workspace.
CMPU2012-Number Theory by Blathnaid Sheridan in Blathnaid's workspace.
CMPU1018_CA1 by Blathnaid Sheridan in Blathnaid's workspace.
Number Theory Practice by cormac breen in cormac's workspace.
CMPU1018_CA_ by Blathnaid Sheridan in Blathnaid's workspace.
CMPU1018 Number Theory Quiz 1 by Blathnaid Sheridan in Blathnaid's workspace.

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Modular Arithmetic: prime multiplication table

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Daniel Mansfield 7 years, 8 months ago

Daniel Mansfield 7 years, 8 months ago

Daniel Mansfield 7 years, 8 months ago

Error in variable testing condition

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Generated value: `integer`

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Number entry

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Modular Arithmetic: prime multiplication table

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Daniel Mansfield 7 years, 8 months ago

Daniel Mansfield 7 years, 8 months ago

Daniel Mansfield 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Number entry

Advanced settings

Generated value: `integer`