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πŸ“

A First Course in Number Theory

✍ Scribed by Alexandru Buium


Year
2019
Tongue
English
Leaves
46
Series
lecture notes
Edition
version 2019-04-26
Category
Library

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No coin nor oath required. For personal study only.

✦ Table of Contents


  1. Introduction 2
  2. The integers 4
  3. Induction 6
  4. Finite sets, finite sums, finite products 7
  5. The rationals 8
  6. Divisibility and Euclid division 10
  7. Polynomial time algorithms 12
  8. Primes 13
  9. Greatest common divisor 14
  10. Unique factorization 15
  11. Applications of unique factorization 17
  12. Congruences: generalities 19
  13. Complete residue systems 20
  14. Residue classes 21
  15. Inverses mod m 22
  16. Groups 23
  17. Linear congruences 25
  18. Systems of linear congruences 25
  19. Fermat’s little theorem 26
  20. Euler’s theorem 27
  21. Polynomial congruences 28
  22. Langrange’s theorem 30
  23. Order 31
  24. Primitive roots 32
  25. Discrete logarithm 33
  26. Legendre symbol 35
  27. Gaussian integers 37
  28. Fundamental Theorem of Arithmetic for Gaussian integers 38
  29. Factoring prime integers in the Gaussian integers 39
  30. Real and complex numbers 40
  31. Algebraic integers 40
  32. Non-unique factorization in Kummer integers 42
  33. Proof of Quadratic Reciprocity 43
  34. Appendix: Cryptography 45

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