Congruences Flashcards

1
Q

How do you write a is congruent to b, mod n?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

When do we write

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What is a residue class?

A

We group a and b from the following into the same class.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

How do you denote a residue class?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What are the residue classes for n=3?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Finish the following proposition.

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Prove the following proposition.

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Can you divide congruences?

A

No

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Finish the following proposition.

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Prove the following proposition.

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Define the complete set of residues.

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Finish the following lemma.

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Prove the following lemma.

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is a linear congruence?

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Prove the following proposition.

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is the method for solving linear congruences of the form ax ≡ b (mod n)?

A

Where :-) equals ax ≡ b (mod n)

17
Q

Finish the following proposition.

A
18
Q

Prove the following proposition.

A
19
Q

What is the name of the theorem that can be used to solve linear systems?

A

Chineese remainder theorem.

20
Q

What is the chineese remainder theorem?

A
21
Q

Prove the following theorem.

A
22
Q

Define Euler’s φ-function.

A
23
Q

What is another way to think of Euler’s φ-function?

A

In other words, it is the number of positive numbers below n which are coprime to n.

24
Q

What is Euler’s theorem?

A
25
Q

Prove the following theorem.

A
26
Q

What is Fermat’s little theorem?

A
27
Q

What is the Lemma about how to calcualte φ(pn)?

A
28
Q

Prove the following Lemma.

A
29
Q

Finish the following proposition.

A
30
Q

Prove the following proposition.

A
31
Q

Finish the following theorem.

A
32
Q

Prove the following theorem.

A
33
Q

Finish the following Lemma.

A
34
Q

Prove the following Lemma.

A
35
Q
A