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Lectures on number theory

Lectures on number theory (Loan 4 times)

Material type
단행본
Personal Author
Hurwitz, Adolf, 1859-1919. Kritikos, Nikolaos, 1894-. Schulz, William C.
Title Statement
Lectures on number theory / presented by Adolf Hurwitz ; edited for publication by Nikolaos Kritikos ; translated with some additional material by William C. Schulz.
Publication, Distribution, etc
New York :   Springer-Verlag,   c1986.  
Physical Medium
xiv, 273 p. ; 24 cm.
Series Statement
Universitext.
ISBN
0387962360 (pbk.) :
General Note
Translated from the German.  
Includes index.  
Bibliography, Etc. Note
Bibliography: p. [265]-271.
Subject Added Entry-Topical Term
Number theory.
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008 850925t19851986nyu b 001 0 eng
010 ▼a 85025093 //r92
020 ▼a 0387962360 (pbk.) : ▼c $19.80 (est.)
040 ▼a DLC ▼c DLC
041 1 ▼a eng ▼h ger
049 1 ▼l 421036137 ▼f 과학
050 0 0 ▼a QA241 ▼b .H85 1986
082 0 0 ▼a 512.7 ▼2 19
090 ▼a 512.77 ▼b H967LE
100 1 ▼a Hurwitz, Adolf, ▼d 1859-1919.
245 1 0 ▼a Lectures on number theory / ▼c presented by Adolf Hurwitz ; edited for publication by Nikolaos Kritikos ; translated with some additional material by William C. Schulz.
260 ▼a New York : ▼b Springer-Verlag, ▼c c1986.
300 ▼a xiv, 273 p. ; ▼c 24 cm.
490 0 ▼a Universitext.
500 ▼a Translated from the German.
500 ▼a Includes index.
504 ▼a Bibliography: p. [265]-271.
650 0 ▼a Number theory.
700 1 0 ▼a Kritikos, Nikolaos, ▼d 1894-.
700 1 0 ▼a Schulz, William C.

Holdings Information

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No. 1 Location Science & Engineering Library/Sci-Info(Stacks2)/ Call Number 512.77 H967LE Accession No. 421036137 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents


CONTENTS
CHAPTER 1. BASIC CONCEPTS AND PROPOSITIONS
  1. The Principle of Descent = 1
  2. Divisibility and the Division A1gorithm = 3
  3. Prime Numbers = 6
  4. Analysis of a Composite Number into a Product of Primes = 8
  5. Divisors of a Natural Number n, Perfect Numbers = 12
  6. Common Divisors and Common Multiples of two or more Natural Numbers = 15
  7. An Alternate Foundation of the Theory of The Greatest Common Divisor = 18
  8. Euclidean Algorithm for the G.C.D. of two Natural Numbers = 21
  9. Relatively Prime Natural Numbers = 23
  10. Applications of the Preceding Theorems = 26
  11. The Function ø(n) of Euler = 32
  12. Distribution of the Prime Numbers in the Sequence of Natural Numbers = 37
    Problems for Chapter 1 = 45
CHAPTER 2 CONGRUENCES
  13. The Concept of Congruence and Basic Properties = 51
  14. Criteria of Divisibility = 53
  15. Further Theorems on Congruences = 56
  16. Residue Classes mod m = 58
  17. The Theorem of Fermat = 60
  18. Generalized Theorem of Fermat = 61
  19. Euler's Proof of the Generalized Theorem of Fermat = 62
  Problems for Chapter 2 = 66
CHAPTER 3. LINEAR CONGRUENCES
  20. The Linear Congruence and its Solution = 68
  21. Systems of Linear Congruences = 71
  22. The Case when the Moduli m1 , m2 , mk of the System of Congruences are pairwise Relatively Prime = 74
  23. Decomposition of a Fraction into a Sum of An Integer and Partial Fractions = 76
  24. Solution of Linear Congruences with the aid of Continued Fractions = 79
  Problems for Chapter 3 = 84
CHAPTER 4. CONGRUENCES OF HIGHER DEGREE
  25. Generalities for Congruence of Degree k > 1 and Study of the Case of a Prime Modulus = 89
  26. Theorem of Wilson = 93
  27. The System {r, r2 ,} of Incongruent Powers Modulo a prime p = 94
  28. Indices = 96
  29. Binomial Congruences = 99
  30. Residues of Powers Mod p = 101
  31. Periodic Decadic Expansions = 103
  Problems for Chapter 4 = 106
CHAPTER 5. QUADRATIC RESIDUES
  32. Quadratic Residues Modulo m = 109
  33. Criterion of Euler and the Legendre Symbol = 109
  34. Study of the Congruence x2 ≡ a (mod pr = 112
  35. Study of the Congruence x2 ≡ a (mod 2k = 116
  36. Study of the Congruence x2 ≡ a (mod m) with (a,m) = l = 120
  37. Generalization of the Theorem of Wilson = 123
  38. Treatment of the Second Problem of §32 = 127
  39. Study of (-1/p) and Applications = 128
  40. The Lemma of Gauss = 129
  41. Study of (2/p) and an application = 133
  42. The Law of Quadratic Reciprocity = 135
  43. Determination of the 0dd Primes p for which (q/p) = 1 with given q = l38
  44. Generalization of the Symbol (a/p) of Legendre by Jacobi = 139
  45. Completion of the Solution of the Second Problem of §32 = 146
  Problems for Chapter 5 = 151
CHAPTER 6. BINARY QUADRATIC FORMS
  46. Basic Notions = 157
  47. Auxiliary Algebraic Forms = 160
  48. Linear Transformation of the Quadratic Form a x2 + 2bxy + c y2 = 161
  49. Substitutions and Computation with them = 162
  50. Unimodular Transformations (or Unimodular Substitutions) = 168
  51. Equivalence of Quadratic Forms = 170
  52. Substitutions Parallel to ( 0 -1 1 0 ) = 172
  53. Reductions of the First Basic Problem of §46 = 174
  54. Reduced Quadratic Forms with Discriminant △ < 0 = 178
  55. The Number of Classes of Equivalent Forms with Discriminant △ < 0 = 184
  56. The Roots of a Quadratic Form = 187
  57. The Equation of Fermat (and of Pell and Lagrange) = 192
  58. The Divisors of a Quadratic Form1 = 98
  59. Equivalence of a form with itself and solution of the Equation of Fermat for Forms with Megative Discriminant △ = 201
  60. The Primitive Representations of an odd Integer by x2 + y2 = 203
  61. The Representation of an Integer m by a Complete System of Forms with given Discriminant △ < 0 = 205
  62. Regular Continued Fractions = 213
  63. Equivalence of Real Irrational Numbers = 219
  64. Reduced Quadratic Forms with Discriminant △ > 0 = 226
  65. The Period of a Reduced Quadratic Form With △ > 0 = 232
  66. Development of Δ in a Continued Fraction = 241
  67. Equivalence of a form with itself and solution of the equation of Fermat for forms with Positive Discriminant △ = 243
  Problems for Chapter 6 = 252
BIBLIOGRAPHY = 265
INDEX = 272

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