Homework Problems

Section

Problems

1.3 Mathematical Induction

7, 8, 18

1.4 Fibonacci Numbers

14

1.5 Divisibility

14, 16, 28, 29, 32

3.1 Prime Numbers

5, 6

3.2 Distribution of Primes

14

3.3 Greatest Common Divisors

5, 6, 16, 18, 24, 30

3.4 Euclidean Algorithm

2 b), 5 b), 7 b)

3.5 Fundamental Theorem of Arithmetic

7, 10, 17, 18, 19, 21, 34

3.6 Factorization Methods & Fermat Numbers

2 a), 3 b), d), 20

3.7 Linear Diophantine Equations

1 a), b), c), d), 2 a), 18

4.1 Introduction to Congruences

5, 9, 25, 28, 29, 30, 34

4.2 Linear Congruences

1 a), b), 6, 8, 12

4.3 Chinese Remainder Theorem

1, 3

5.2 The Perpetual Calendar

1, 2 d), j), o), 3, 6

6.1 Wilson's Theorem & Fermat's Little Theorem

5, 11, 16, 20, 28, 30, 48

6.2 Pseudoprimes

4, 5, 8

6.3 Euler's Theorem

2, 4, 8, 11c)

7.1 Euler's Phi-Function

2 e), 5, 11, 12, 16, 17, 26

7.2 Sum and Number of Divisors

1 c), 2 c), 3, 4, 5 a), 6 e), 8, 9, 12, 40

7.3 Perfect Numbers & Mersenne Primes 4 a), 25, 26
7.4 Möbius Inversion 1 e), f), 14, 15, 16 a), 30, 31, 32
9.1 Order of Integers & Primitive Roots 1 b), 6 c), 8, 14, 18, 20
9.2 Primitive Roots for Primes 5, 10, 11

9.3 Existence of Primitive Roots

5 a), 9, 12, 13, 14

9.4 Discrete Logarithms & Index Arithmetic

3 a), 8, 9, 10

11.1 Quadratic Residues and Nonresidues 1 b), 4, 7, 10, 28 a)
11.2 Law of Quadratic Reciprocity 1 a), c), f), 4, 6