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OverviewLike other introductions to number theory, this text includes the usual curtsy to divisibility theory, the bow to congruence, and the little chat with quadratic reciprocity. It also includes proofs of results such as Lagrange's Four Square Theorem, the theorem behind Lucas's test for perfect numbers, the theorem that a regular n-gon is constructible just in case o(n) is a power of 2, the fact that the circle cannot be squared, Dirichlet's theorem on primes in arithmetic progressions, the Prime Number Theorem and Rademacher's partition theorem. The proofs of these theorems have been made as elementary as possible. The book includes presentations of palindromic simple continued fractions, an elementary solution of Lucas's square pyramid problem, Baker's solution for simultaneous Fermat equations, an elementary proof of Fermat's polygonal number conjecture, and the Lambek-Moser-Wild theorem. Full Product DetailsAuthor: W.S. AnglinPublisher: Springer Imprint: Springer Edition: 1995 ed. Volume: 8 Dimensions: Width: 15.50cm , Height: 2.30cm , Length: 23.50cm Weight: 0.854kg ISBN: 9780792332879ISBN 10: 0792332873 Pages: 390 Publication Date: 31 January 1995 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of Contents1 Propaedeutics.- 1.1 Mathematical Induction.- 1.2 Bernoulli Numbers.- 1.3 Primes.- 1.4 Perfect Numbers.- 1.5 Greatest Integer function.- 1.6 Pythagorean Triangles.- 1.7 Diophantine Equations.- 1.8 Four Square Theorem.- 1.9 Fermat’s Last Theorem.- 1.10 Congruent Numbers.- 1.11 Möbius function.- 2 Simple Continued Fractions.- 2.1 Convergents and Convergence.- 2.2 Uniqueness of SCF Expansions.- 2.3 SCF Expansions of Rationals.- 2.4 Farey Series.- 2.5 Ax + By = C.- 2.6 SCF Approximations.- 2.7 SCF Expansions of Quadratic Surds.- 2.8 Periodic SCF Expansions.- 2.9 Pell Equation.- 2.10 Prefaced Palindromes.- 3 Congruence.- 3.1 Basic Properties.- 3.2 Euler’s ?-Function.- 3.3 Primitive Roots.- 3.4 Decimal Expansions.- 3.5 x2 ? R (mod C).- 3.6 Palindromic SCF’s.- 3.7 Sums of Two Squares.- 3.8 Quadratic Residues.- 3.9 Theorema Aureum.- 3.10 Jacobi Symbol.- 3.11 More on x2 ? R (mod C).- 3.12 Ax2 + By = C.- 4 x2?Ry2 = C.- 4.1 SCF Solution.- 4.2 Recursive Formulas for Solutions.- 4.3 Ax2 + Bxy + Cy2 + Dx + Ey = F.- 4.4 Square Pyramid Problem.- 4.5 Lucas’s Test for Perfect Numbers.- 4.6 Simultaneous Fermat Equations.- 5 Classical Construction Problems.- 5.1 Euclidean Constructions.- 5.2 Fields and Vector Spaces.- 5.3 Limits of Ruler and Compass Construction.- 5.4 Gauss’s Constructions.- 5.5 Fermat Primes.- 5.6 The Transcendence of ?.- 6 The Polygonal Number Theorem.- 6.1 Gaussian Forms.- 6.2 Ternary Quadratic Form Matrices.- 6.3 Omega Kernel or Square Forms.- 6.4 Ambiguous or Self-Inverse Forms.- 6.5 Sums of Triangular Numbers.- 6.6 Cauchy’s Proof.- 7 Analytic Number Theory.- 7.1 Characters.- 7.2 Dirichlet Series.- 7.3 Mangoldt function.- 7.4 L(1,X) ? 0.- 7.5 Dirichlet’s Theorem on Primes in AP.- 7.6 How Many Pythagorean Triangles?.- 7.7 Prime Preliminaries.-7.8 Prime Number Theorem Proof.- 7.9 Partitions.- 7.10 Euler’s Power Series.- 7.11 A Fractal Path of Ford Circles.- 7.12 Möbius Transformations.- 7.13 Dedekind Sums.- 7.14 Eta function.- 7.15 Bessel Functions Avoided.- 7.16 Rademacher’s Proof.- 7.17 Numerical Calculations.- A Appendix: Answers to Selected Exercises.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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