| Preface 1 The Fibonacci Numbers and the Aretic Ocean 1 Basic definitions A Lucas sequences B Speciallucas sequences C Generalizations 2 Basic properties A binet's formulas B Degenerate Lucas sequences C Growth and numerical calculations D Algebraic relations. E Divisibility properties 3 Prime divisors of Lucas sequences A The sets P(U), P(V), and the rank ofappearance B Primitive factors of Lucas sequences 4 Primes in Lucas sequences 5 Powers and powerful numbers in Lucas sequences A General theorems for powers B Explicit determination in special sequences C Uniform explicit determination ofmultiples, squares, and square-classes forcertain families of Lucas sequences D Powerful numbers in Lucas sequences 2 Representation of Real Numbers by Means ofFibonacci N-tubers 3 Prime Number Records 4 Selling Primes 5 Euler's Famous Prime Generating Polynomial 1 Quadratic extensions 2 Rings of integers 3 Discriminant 4 Decomposition of primes A Properties of the norm 5 Units 6 The class number A Calculation of the class n, lmber B Determination of all quadratic fields withclass number 1 7 The main theorem 6 Gauss and the Class Number Problem 1 Introduction 2 Highlights of Gauss' life 3 Brief historical background 4 Binary quadratic forms 5 The fundamental problems 6 Equivalence of forms 7 Conditional solution of the fundamental problems 8 Proper equivalence classes of definite forms A Another numerical example 9 Proper equivalence classes of indefinite forms A Another numerical example 10 The automorph of a primitive form 11 Composition of proper equivalence classes ofprimitive forms |
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