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Viser: Elementary Number Theory
Elementary Number Theory Vital Source e-bog
Gareth A. Jones og Josephine M. Jones
(2012)
Elementary Number Theory Vital Source e-bog
Gareth A. Jones og Josephine M. Jones
(2012)
Elementary Number Theory
Gareth A. Jones og Josephine M. Jones
(1998)
Sprog: Engelsk
Detaljer om varen
- Vital Source searchable e-book (Reflowable pages)
- Udgiver: Springer Nature (December 2012)
- Forfattere: Gareth A. Jones og Josephine M. Jones
- ISBN: 9781447106135
Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.
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Print: 2 sider kan printes ad gangen
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Detaljer om varen
- Vital Source 365 day rentals (dynamic pages)
- Udgiver: Springer Nature (December 2012)
- Forfattere: Gareth A. Jones og Josephine M. Jones
- ISBN: 9781447106135R365
Bookshelf online: 5 år fra købsdato.
Bookshelf appen: 5 år fra købsdato.
Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: 2 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)
Detaljer om varen
- 1. Udgave
- Paperback
- Udgiver: Springer London, Limited (Juli 1998)
- Forfattere: Gareth A. Jones og Josephine M. Jones
- ISBN: 9783540761976
1. Divisibility. -
1.
1 Divisors. -
1.
2 Bezout's identity. -
1.
3 Least common multiples. -
1.
4 Linear Diophantine equations. -
1.
5 Supplementary exercises. -
2. Prime Numbers. -
2.
1 Prime numbers and prime-power factorisations. -
2.
2 Distribution of primes. -
2.
3 Fermat and Mersenne primes. -
2.
4 Primality-testing and factorisation. -
2.
5 Supplementary exercises. -
3. Congruences. -
3.
1 Modular arithmetic. -
3.
2 Linear congruences. -
3.
3 Simultaneous linear congruences. -
3.
4 Simultaneous non-linear congruences. -
3.
5 An extension of the Chinese Remainder Theorem. -
3.
6 Supplementary exercises. -
4. Congruences with a Prime-power Modulus. -
4.
1 The arithmetic of ?p. -
4.
2 Pseudoprimes and Carmichael numbers. -
4.
3 Solving congruences mod (pe). -
4.
4 Supplementary exercises. -
5. Euler's Function. -
5.
1 Units. -
5.
2 Euler's function. -
5.
3 Applications of Euler's function. -
5.
4 Supplementary exercises. -
6. The Group of Units. -
6.
1 The group Un. -
6.
2 Primitive roots. -
6.
3 The group Une, where p is an odd prime. -
6.
4 The group U2e. -
6.
5 The existence of primitive roots. -
6.
6 Applications of primitive roots. -
6.
7 The algebraic structure of Un. -
6.
8 The universal exponent. -
6.
9 Supplementary exercises. -
7. Quadratic Residues. -
7.
1 Quadratic congruences. -
7.
2 The group of quadratic residues. -
7.
3 The Legendre symbol. -
7.
4 Quadratic reciprocity. -
7.
5 Quadratic residues for prime-power moduli. -
7.
6 Quadratic residues for arbitrary moduli. -
7.
7 Supplementary exercises. -
8. Arithmetic Functions. -
8.
1 Definition and examples. -
8.
2 Perfect numbers. -
8.
3 The Mobius Inversion Formula. -
8.
4 An application of the Mobius Inversion Formula. -
8.
5 Properties of the Mobius function. -
8.
6 The Dirichlet product. -
8.
7 Supplementary exercises. -
9. The Riemann Zeta Function. -
9.
1 Historical background. -
9.
2 Convergence. -
9.
3 Applications to prime numbers. -
9.
4 Random integers. -
9.
5 Evaluating ?(2). -
9.
6 Evaluating ?(2k). -
9.
7 Dirichlet series. -
9.
8 Euler products. -
9.
9 Complex variables. -
9.
10 Supplementary exercises. -
10. Sums of Squares. -
10.
1 Sums of two squares. -
10.
2 The Gaussian integers. -
10.
3 Sums of three squares. -
10.
4 Sums of four squares. -
10.
5 Digression on quaternions. -
10.
6 Minkowski's Theorem. -
10.
7 Supplementary exercises. -
11. Fermat's Last Theorem. -
11.
1 The problem. -
11.
2 Pythagoras's Theorem. -
11.
3 Pythagorean triples. -
11.
4 Isosceles triangles and irrationality. -
11.
5 The classification of Pythagorean triples. -
11.
6 Fermat. -
11.
7 The case n =
4. -
11.
8 Odd prime exponents. -
11.
9 Lame and Kummer. -
11.
10 Modern developments. -
11.
11 Further reading. - Solutions to Exercises. -
Index of symbols. -
Index of names.