# Book:J. Hunter/Number Theory

## J. Hunter: Number Theory

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

### 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

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## Source work progress

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