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Math 1020: Applied Elementary Number Theory : Homework **

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Homework 1 -- due Sept 6
1. Section 1-1: Exercise 1

2. Section 1-1: Exercise 6

3. Section 1-1: Exercise 10

4. Section 1-2: Exercise 4

5. Section 1-2: Exercise 5

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Homework 2 -- due Sept 11
1. Section 2-1: Exercise 4

2. Section 2-1: Exercise 6

3. Section 2-2: Exercise 1 (use Euclid's algorithm)

4. Section 2-2: Exercise 4

5. Section 2-2: Exercise 12

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Homework 3 -- due Sept 18
1. Section 2-3: Exercise 1

2. Section 2-4: Exercise 5

3. Section 2-4: Exercise 12

4. Section 3-1: Exercise 1 and 2

5. Section 3-1: Exercise 3 and 6

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Homework 4 -- due Sept 25
1. Section 3-2: Exercise 2 and 3

2. Section 3-3: Exercise 1

3. Section 3-4: Exercise 3

4. Section 4-2: Exercise 1 and 2

5. Section 4-3: Exercise 1

Bonus Problem (5 pts): Section 4-2: Exercise 3

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Homework 5 -- due Oct 2
1. Section 5-1: Exercise 2 and 3

2. Section 5-2: Exercise 2

3. Section 5-2: Exercise 3

4. Section 5-3: Exercise 1

5. Section 5-3: Exercise 2

Bonus Problem (10 pts): Section 5-2: Exercise 20

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Homework 6 -- due Oct 10
1. Section 5-2: Exercise 4

2. Section 5-3: Exercise 3 and 4

3. Section 5-4: Exercise 1 and 2

4. Section 6-1: Exercise 1 and 4

5. Section 6-2: Exercise 2 and 3

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Homework 7 -- due Oct 16
1. Section 6-4: Exercise 2

2. Section 6-4: Exercise 8

3. Section 6-4: Exercise 10 and 11

4. Section 6-4: Exercise 14

5. Section 7-1: Exercise 1 and 2

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Homework 8 -- due Oct 23
1. Section 6-2: Exercise 10 and 11

2. Section 7-1: Exercise 6

3. Section 7-2: Exercise 11

4. Section 8-1: Exercise 1 and 2

5. Section 8-1: Exercise 4 and 5

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Homework 9 -- due Oct 30
1. Section 5-2: Exercise 22

2. Section 7-2: Exercise 15 and 16

3. Section 8-1: Exercise 9 and 10

4. Section 8-2: Exercise 2

5. Section 8-2: Exercise 6

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Homework 10 -- due Nov 6
1. Section 5-3: Exercise 6

2. Section 9-2: Exercise 1 and Exercise 2

3. Section 9-3: Exercise 1 and Exercise 2

4. Section 9-3: Exercise 5

5. Section 9-4: Exercise 1 and Exercise 2

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Homework 11 -- due Nov 13
1. Section 5-4: Exercise 3 and 4

2. Section 10-1: Exercise 1 and Exercise 2

3. Section 10-1: Exercise 4

4. Section 10-1: Exercise 5

5. Section 10-2: Exercise 1

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Homework 12 -- due Nov 20
1. Section 5-2: Exercise 9

2. Section 10-2: Exercise 2

3. Section 11-1: Exercise 1 and Exercise 2

4. Section 11-2: Exercise 1

5. Section 11-2: Exercise 2

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Homework 13 -- due November 27
1. Section 5-2: Exercise 11

2. Section 9-3: Exercise 4

3. Section 12-2: Exercise 1

4. Section 12-2: Exercise 2 and Exercise 3

5. Section 12-3: Exercise 1

Bonus Problem (30 pts): Which natural numbers can be represented as
sums of 3 squares?

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Homework 14 -- due Dec 4
1. Section 13-1: Prove, with all details, the formula (13-1-2)

2. Section 13-1: Prove, with all details, the formula (13-1-3)

3. Section 13-1: Exercise 1

4. Section 13-1: Exercise 2

5. Section 13-1: Exercise 3