Book:J. Hunter/Number Theory

J. Hunter: Number Theory

Published $\text {1964}$, Oliver and Boyd

Subject Matter

• Number Theory

Contents

Preface

chapter $\text{I}$ NUMBER SYSTEMS AND ALGEBRAIC STRUCTURES

1. Introduction

2. The positive integers

3. Equivalence relations

4. The set of all integers

5. The rational numbers

6. Algebraic structures

Examples

chapter $\text{II}$ DIVISION AND FACTORISATION PROPERTIES

7. Division identities for the integers

8. Representation in the scale of $g$

9. Least common multiple, greatest common divisor, Euclidean algorithm

10. Prime numbers, unique factorisation theorem

11. Relatively prime numbers, Euler's function $\phi$

12. Multiplicative arithmetical functions, the Möbius function $\mu$, the inversion formula

Examples

chapter $\text{III}$ CONGRUENCES

13. Congruence notation, operations on congruences

14. Residue sets (mod $m$)

15. Euler's Theorem, order of $a$ (mod $m$)

16. Linear congruences

17. The ring of congruence classes (mod $m$)

18. Algebraic interpretation of Theorems $22$, $23$ and $24$

Examples

chapter $\text{IV}$ ALGEBRAIC CONGRUENCES AND PRIMITIVE ROOTS

19. Algebraic congruences

20. Algebraic congruences (mod $p$)

21. Algebraic congruences with composite modulus

22. Primitive roots

23. Indices

Examples

chapter $\text{V}$ QUADRATIC RESIDUES

24. $n$-th power residues

25. The Legendre symbol $\paren {a / p}$

26. The law of quadratic reciprocity

27. The Jacobi symbol $\paren {a / b}$

Examples

chapter $\text{VI}$ REPRESENTATION OF INTEGERS BY BINARY QUADRATIC FORMS

28. Definitions and notation

29. Unimodular matrices and transformations

30. Equivalence classes of binary quadratic forms

31. Binary quadratic forms of given discriminant $d$

32. Representation of integers by binary quadratic forms

33. Representation of an integer as a sum of two squares

Examples

chapter $\text{VII}$ SOME DIOPHANTINE EQUATIONS

34. Diophantine equations

35. Linear diophantine equations

36. The equation $x^2 + y^2 = z^2$, and related equations

37. Fermat's Last Theorem, the equation $x^4 + y^4 = z^2$

Examples

Index

Next

Source work progress

• 1964: J. Hunter: Number Theory ... (previous) ... (next): Chapter $\text {I}$: Number Systems and Algebraic Structures: $2$. The positive integers

$1$-based exposition of Peano structure to be embarked upon.