Book:J. Hunter/Number Theory
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J. Hunter: Number Theory
Published $\text {1964}$, Oliver and Boyd
Subject Matter
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
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.