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 |