**HMC Math 175: Number Theory (Spring, 2000)**

Homework

### Assignment #10 (due Mon 5/1):

**Section 6.3:** 1 (+,* only), 6

**Section 7.1:** 1, 3, 4, 5

**Section 7.2:** 1

**Section 7.3:** 2

### Assignment #9 (due Mon 4/10):

**Section 5.3:** 2, 4, 7, 8, 10

**Section 6.1:** 1, 2, 7

**9A**: Also do the problems in this GIF.

### Assignment #8 (due Mon 4/3):

**Section 4.3:** 1, 3, 5, 7, 8, 15

**8A**: Determine the Mobius function of a linearly ordered set (a total order). What does the Mobius inversion formula say in this case?

**8B**: Determine the Mobius function of the poset P=(X,|), for X = {divisor of 12} under the "divides" relation.

**Note:** You may use MATLAB or some other computer package to compute matrix inverses for 8A and 8B.

### Assignment #7 (due Mon 3/27):

**Section 4.1:** 3ae, 6, 7, 13, 15

**Section 4.2:** 3, 5, 10, 12, 16

**7A**: What day of the week was John Denver born on?

### Assignment #6 (due Mon 3/6):

**Section 3.1:** 5, 8be, 12, 23

**Section 3.2:** 4adf, 8, 11, 17

**Section 3.3:** 4, 5, 15

Note: On 3.3.15, regarding the Hint... I used (3/p) as well as (2/p) & (5/p)

**6A**: Prove parts (2)-(5) of Theorem 3.1 (you may use part (1)).

### Assignment #5 (due Mon 2/28):

**Section 2.4:** 14ab, 19, 20

**Section 2.6:** 8, 9, 10

**Section 2.7:** 1a, 3, 4

**5A**: Also solve:

x^3 + x + 10 = 0 (mod 25)

x^3 + 2x + 12 = 0 (mod 7^3)

(Use the methods of Section 2.6)

### Assignment #4 (due Mon 2/21):

**Section 2.3:** 1, 6, 7, 14, 18, 19, 29, 40

(For #18, give an example when k=3)

**Section 2.4:** 5, 6, 9, 10, 11

### Assignment #3 (due Mon 2/14):

**Section 2.1:** 14, 15, 25, 44

**Section 2.2:** 5abcd, 8, 9, 14

Also do problems
3A and
3B (as in, "click here to view them").

(Note: in 3A, there are several "prove" requests. You need only do the one following the "3A" label. The rest are special cases, and are only included as hints in proving the general case.)

### Assignment #2 (due Fri 2/4):

**Section 1.4:** 4, 8 (just do one of the three... pick your favorite!)

**Section 2.1:** 5, 6, 12, 18 (see proof of Thm 2.12), 22, 24, 26, 29, 39, 54a

### Assignment #1 (due Fri 1/28):

**Section 1.2:** 2, 7, 12, 29, 45, 46, 50

**Section 1.3:** 1, 4, 11, 16, 39

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