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Solving a system of simultaneous congruences using the Chinese Remainder Theorem.
An explore mode question which allows you to write a solution straight away, or break it down into steps.
After solving a system of three congruences, you can ask for a new problem with more congruences.
Metadata
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England schools
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England university
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Scotland schools
Taxonomy: mathcentre
Taxonomy: Kind of activity
Taxonomy: Context
Contributors
History
Christian Lawson-Perfect 7 months ago
Published this.Christian Lawson-Perfect 7 months ago
Created this as a copy of Solve three congruences using Chinese Remainder Theorem - MAS3214.There is only one version of this question that you have access to.
There is one other version that you do not have access to.
| Name | Type | Generated Value |
|---|
| num_rows | integer |
3
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| n_range | range |
5..15
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| ns | list |
[ 7, 13, 15 ]
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| rs | list |
[ 1, 8, 4 ]
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| ys | list |
[ 195, 105, 91 ]
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| zs | list |
[ 6, 1, 1 ]
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| solution | number |
1009
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| solutions | list |
[ 1, 8, 1009 ]
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| first_congruence_expression | expression |
7n + 1
|
| Name | Type | Generated Value |
|---|
| congruences_latex | string |
\begin{align}
x \equiv 1 &\mod
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| congruences_in_words | html |
HTML node
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| two_congruences_table | html |
HTML node
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| Name | Type | Generated Value |
|---|
| n | number |
7
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||||
| r | integer |
1
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| had_help | boolean |
false
|
Generated value: integer
3
→ Used by:
- ns
- solutions
- "Write a number satisfying the congruences" - next part availability condition
- "Write a number satisfying the congruences" - variable replacement
- "Write a number satisfying the congruences" - variable replacement
Parts
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Prompt
Information only
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Write a number satisfying the congruences
Number entry
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Help
Information only
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Solve the first congruence
Number entry
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Write an expression for numbers satisfying the first congruence
Mathematical expression
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Solve the second congruence
Number entry
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Help with solving two congruences
Information only
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About the theorem
Information only
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| Mathematical expression | ||
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This question is used in the following exam: