## Math 1020: Applied Elementary Number Theory : Homework

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

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

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

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

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

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

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

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

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

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

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

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

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?

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