An Introduction to Number Theory
Harold Stark

Possible homework exercises.  I've looked through the exercises in the book and selected a
bunch of them that look good for homework exercises.  There are more here than I'll actually
assign, but they look good, so I might use some of them on quizzes or tests.

I'm substituting public-key cryptography for chapter 4's magic squares, so I'll have to
come up with some exercises on public-key cryptography.


Chapter 1  An introduction to number theory
  1.1  An introduction to number theory
  1.2  Some elementary properties of divisibility
       p. 14 Misc. exercises: 1, 2, 3, 4, 5, 8, 9
  
Chapter 2  The Euclidean algorithm and unique factorization
  2.1  The Euclidean algorithm
       p. 25: 2, 3, 4, 5, 6, 11, 12, 13
  2.2  The fundamenatal theorem of arithmetic
       p. 32: 5, 7, 8, 12, 13, 14, 15
  2.3  Applications of the fundamental theorem
       p. 35: 1, 2
  2.4  Multiplicative functions
       p. 43: 1, 2, 3, 5, 6, 7, 8
  2.5  Linear Diophantine equations
       p. 47: 1-10, 12
       p. 48 Misc. exercises: 2, 3, 7, 11
  
Chapter 3  Congruences
  3.1  Introduction
       p. 54: 1-5, 7, 8, 10
  3.2  Fundamental properties of congruences
       p. 63: 1, 2, 4, 5, 6, 8, 9, 10, 13, 17, 19-21, 35
  3.3  Linear congruence equations
       p. 76: 1-3, 7-9, 11-13, 17, 20
  3.4  Reduced residue systems and Euler's phi function
       p. 82: 1, 2, 4, 10
  3.5  More on Euler's phi function
       p. 86: 1, 2, 6, 7
  3.6  Polynomial congruences
       (We'll only survey this section.)
  3.7  Primitive roots
       p. 106: 2, 4, 5, 9, 12
       p. 108 Misc. exercises: 8, 12, 15, 24-26
       
Public-key cryptography
       Exercises yet to be selected
  
Chapter 5  Diophantine equations
  5.1  Introduction
       p. 148: 1, 4
  5.2  The use of congruences in solving Diophantine equations
       p. 151: 3, 7, 11
  5.3  Pythagorean triples
       p. 155: 1, 2, 7
  5.4  Fermat's method of descent
       p. 161: 3, 4, 5
       p. 162 Misc. exercises: 2, 5, 7

Chapter 6  Numbers, rational and irrational
  6.1  Rational numbers
       p. 169: 3-6, 7, 8, 9
  6.2  Irrational numbers
       p. 171: 1, 2, 3
  6.3  Lieuville's theorem and transcendental numbers
       (We'll only survey section 6.3)
       p. 177 Misc. exercises: 3, 7

Chapter 7  Continued fractions from a geometric viewpoint
  7.1  Introduction
       p. 185: 3, 5
  7.2  The continued fraction algorithm
       p. 196: 4, 5-7
  7.3  Computation of a(sub)n
       p. 208: 1-5, 8
  7.4  The best approximations
       p. 221: 3, 7, 10
  7.5  A commentary of proof by picture
  7.6  Periodic continued fractions
       p. 238: 2-8, 11, 12
  7.7  The Fermat-Pell equation and the continued fraction
       expansion of square roots
       p. 245: 1-3, 6-8, 11, 12
       p. 246 Misc. exercises: 2, 7