Springer Undergraduate Mathematics Ser.: Elementary Number Theory by Josephine M. Jones and Gareth A. Jones (1998, Trade Paperback)

Springer London, The Limited

3540761977

9783540761976

869465

Josephine M. Jones, Gareth A. Jones

Elementary Number Theory

Trade Paperback

English

Springer Undergraduate Mathematics Ser.

1998

Textbook

Xiv, 302 Pages

9.3in

0.3in

7in

34.6 Oz

1 Vol.

Qa241-247.5

From the reviews: BULLETIN OF MATHEMATICS BOOKS "?as a nice concluding chapter on Fermat? Last Theorem, with a brief discussion on the coup de grace." G.A. Jones and J.M. Jones Elementary Number Theory "A welcome addition . . . a carefully and well-written book."--THE MATHEMATICAL GAZETTE "This book would make an excellent text for an undergraduate course on number theory." --MATHEMATICAL REVIEWS, From the reviews: BULLETIN OF MATHEMATICS BOOKS "?as a nice concluding chapter on Fermat? Last Theorem, with a brief discussion on the coup de grace."   G.A. Jones and J.M. Jones Elementary Number Theory "A welcome addition . . . a carefully and well-written book."--THE MATHEMATICAL GAZETTE "This book would make an excellent text for an undergraduate course on number theory." --MATHEMATICAL REVIEWS, From the reviews:BULLETIN OF MATHEMATICS BOOKS"?as a nice concluding chapter on Fermat? Last Theorem, with a brief discussion on the coup de grace." G.A. Jones and J.M. JonesElementary Number Theory"A welcome addition . . . a carefully and well-written book."-THE MATHEMATICAL GAZETTE"This book would make an excellent text for an undergraduate course on number theory."-MATHEMATICAL REVIEWS, From the reviews: BULLETIN OF MATHEMATICS BOOKS "?as a nice concluding chapter on Fermat? Last Theorem, with a brief discussion on the coup de grace."   G.A. Jones and J.M. Jones Elementary Number Theory "A welcome addition . . . a carefully and well-written book."-THE MATHEMATICAL GAZETTE "This book would make an excellent text for an undergraduate course on number theory." -MATHEMATICAL REVIEWS

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.

1998

Number Theory

97-041193

512/.7

Scholarly & Professional

21

Yes

Mathematics