An Introduction to Number Theory

by J. J. P. Veerman

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These notes are intended for a graduate course in Number Theory. No prior familiarity with number theory is assumed. Chapters 1-6 represent approximately 1 trimester of the course. Eventually we intend to publish a full year (3 trimesters) course on number theory.

Description from LibreTexts.

Publisher
Portland State University
Subjects
Mathematics, Combinatorics and Discrete Mathematics
Licence
CC BY-NC, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: A Quick Tour of Number Theory
  7. 1.1: Divisors and Congruences
  8. 1.2: Rational and Irrational Numbers
  9. 1.3: Algebraic and Transcendental Numbers
  10. 1.4: Countable and Uncountable Sets
  11. 1.5: Exercises
  12. 2: The Fundamental Theorem of Arithmetic
  13. 2.1: Bézout's Lemma
  14. 2.2: Corollaries of Be ́zout’s Lemma
  15. 2.3: The Fundamental Theorem of Arithmetic
  16. 2.4: Corollaries of the Fundamental Theorem of Arithmetic
  17. 2.5: The Riemann Hypothesis
  18. 2.6: Exercises
  19. 3: Linear Diophantine Equations
  20. 3.1: The Euclidean Algorithm
  21. 3.2: A Particular Solution of ax+by = c
  22. 3.3: Solution of the Homogeneous equation ax+by = 0
  23. 3.4: The General Solution of ax+by = c
  24. 3.5: Recursive Solution of x and y in the Diophantine Equation
  25. 3.6 Exercises
  26. 4: Number Theoretic Functions
  27. 4.1: Multiplicative Functions
  28. 4.2: Additive Functions
  29. 4.3: Mobius inversion
  30. 4.4: Euler’s Phi or Totient Function
  31. 4.5: Dirichlet and Lambert Series
  32. 4.6: Exercise
  33. 5: Modular Arithmetic and Primes
  34. 5.1: Modular Arithmetic
  35. 5.2: Euler's Method
  36. 5.3: Fermat’s Little Theorem and Primality Testing
  37. 5.4: Fermet and Mersenne Primes
  38. 5.5: Division in \(\mathbb{Z}_{b}\)
  39. 5.6: Exercises
  40. 6: Continued Fractions
  41. 6.1: The Gauss Map
  42. 6.2: New Page
  43. 6.3: New Page
  44. 6.4: New Page
  45. 6.5: New Page
  46. 6.6: New Page
  47. Back Matter
  48. Index
  49. Glossary
  50. Detailed Licensing