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Appendix B Hints and Answers to Selected Exercises

1 Preliminaries
1.4 Exercises

2 The Integers
2.4 Exercises

2.4.17. Fibonacci Numbers.

3 Groups
3.5 Exercises

4 Cyclic Groups
4.5 Exercises

5 Permutation Groups
5.4 Exercises

6 Cosets and Lagrange's Theorem
6.5 Exercises

7 Introduction to Cryptography
7.4 Exercises

8 Algebraic Coding Theory
8.6 Exercises

9 Isomorphisms
9.4 Exercises

10 Normal Subgroups and Factor Groups
10.4 Exercises

11 Homomorphisms
11.4 Exercises

12 Matrix Groups and Symmetry
12.4 Exercises

13 The Structure of Groups
13.4 Exercises

14 Group Actions
14.5 Exercises

15 The Sylow Theorems
15.4 Exercises

16 Rings
16.7 Exercises

17 Polynomials
17.5 Exercises

17.5.20. Cyclotomic Polynomials.

18 Integral Domains
18.4 Exercises

19 Lattices and Boolean Algebras
19.5 Exercises

20 Vector Spaces
20.5 Exercises

20.5.15. Linear Transformations.

20.5.17. Direct Sums.

21 Fields
21.5 Exercises

22 Finite Fields
22.4 Exercises

22.4.24. Wilson's Theorem.

23 Galois Theory
23.5 Exercises