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Bibliographic Details
Title:	Elementary number theory
From:	Gareth A. Jones and J. Mary Jones
Person:	Jones, Gareth A. 1946- Verfasser aut Jones, Josephine Mary
Main Authors:	Jones, Gareth A. 1946- (Author), Jones, Josephine Mary 1946- (Author)
Format:	Book
Language:	German
Published:	London ; Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Springer 1998
Series:	Springer undergraduate mathematics series
Subjects:	Number theory Zahlentheorie Lehrbuch
Online Access:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007888853&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XIV, 301 S. graph. Darst.
ISBN:	3540761977

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MARC


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Record in the Search Index

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adam_text	CONTENTS NOTES TO THE READER XIII 1. DIVISIBILITY 1 1.1 DIVISORS 2 1.2 BEZOUT S IDENTITY 7 1.3 LEAST COMMON MULTIPLES 12 1.4 LINEAR DIOPHANTINE EQUATIONS 13 1.5 SUPPLEMENTARY EXERCISES 16 2. PRIME NUMBERS 19 2.1 PRIME NUMBERS AND PRIME-POWER FACTORISATIONS 19 2.2 DISTRIBUTION OF PRIMES 25 2.3 FERMAT AND MERSENNE PRIMES 30 2.4 PRIMALITY-TESTING AND FACTORISATION 32 2.5 SUPPLEMENTARY EXERCISES 35 3. CONGRUENCES 37 3.1 MODULAR ARITHMETIC 37 3.2 LINEAR CONGRUENCES 46 3.3 SIMULTANEOUS LINEAR CONGRUENCES 52 3.4 SIMULTANEOUS NON-LINEAR CONGRUENCES 57 3.5 AN EXTENSION OF THE CHINESE REMAINDER THEOREM 59 3.6 SUPPLEMENTARY EXERCISES 62 4. CONGRUENCES WITH A PRIME-POWER MODULUS 65 4.1 THE ARITHMETIC OF Z P 65 4.2 PSEUDOPRIMES AND CARMICHAEL NUMBERS 72 ELEMENTARY NUMBER THEORY 4.3 SOLVING CONGRUENCES MOD (P E ) 78 4.4 SUPPLEMENTARY EXERCISES 82 5. EULER S FUNCTION 83 5.1 UNITS ; 83 5.2 EULER S FUNCTION 85 5.3 APPLICATIONS OF EULER S FUNCTION 92 5.4 SUPPLEMENTARY EXERCISES 96 6. THE GROUP OF UNITS 97 6.1 THE GROUP U N 97 6.2 PRIMITIVE ROOTS 99 6.3 THE GROUP U P E, WHERE P IS AN ODD PRIME 103 6.4 THE GROUP U 2 * 106 6.5 THE EXISTENCE OF PRIMITIVE ROOTS 108 6.6 APPLICATIONS OF PRIMITIVE ROOTS 110 6.7 THE ALGEBRAIC STRUCTURE OF U N 113 6.8 THE UNIVERSAL EXPONENT 116 6.9 SUPPLEMENTARY EXERCISES 117 7. QUADRATIC RESIDUES 119 7.1 QUADRATIC CONGRUENCES 119 7.2 THE GROUP OF QUADRATIC RESIDUES 120 7.3 THE LEGENDRE SYMBOL 123 7.4 QUADRATIC RECIPROCITY 130 7.5 QUADRATIC RESIDUES FOR PRIME-POWER MODULI 135 7.6 QUADRATIC RESIDUES FOR ARBITRARY MODULI 138 7.7 SUPPLEMENTARY EXERCISES 140 8. ARITHMETIC FUNCTIONS 143 8.1 DEFINITION AND EXAMPLES 143 8.2 PERFECT NUMBERS 146 8.3 THE MOBIUS INVERSION FORMULA 148 8.4 AN APPLICATION OF THE MOBIUS INVERSION FORMULA 152 8.5 PROPERTIES OF THE MOBIUS FUNCTION 154 8.6 THE DIRICHLET PRODUCT 157 8.7 SUPPLEMENTARY EXERCISES 162 9. THE RIEMANN ZETA FUNCTION 163 9.1 HISTORICAL BACKGROUND 163 9.2 CONVERGENCE 165 9.3 APPLICATIONS TO PRIME NUMBERS 166 CONTENTS XI 9.4 RANDOM INTEGERS 170 9.5 EVALUATING ((2) 174 9.6 EVALUATING ((2K) 176 9.7 DIRICHLET SERIES 179 9.8 EULER PRODUCTS 182 9.9 COMPLEX VARIABLES 185 9.10 SUPPLEMENTARY EXERCISES 188 10. SUMS OF SQUARES 191 10.1 SUMS OF TWO SQUARES 191 10.2 THE GAUSSIAN INTEGERS 196 10.3 SUMS OF THREE SQUARES 201 10.4 SUMS OF FOUR SQUARES 202 10.5 DIGRESSION ON QUATERNIONS 205 10.6 MINKOWSKI S THEOREM 206 10.7 SUPPLEMENTARY EXERCISES 214 11. FERMAT S LAST THEOREM 217 11.1 THE PROBLEM 217 11.2 PYTHAGORAS S THEOREM 218 11.3 PYTHAGOREAN TRIPLES 219 11.4 ISOSCELES TRIANGLES AND IRRATIONALITY 221 11.5 THE CLASSIFICATION OF PYTHAGOREAN TRIPLES 223 11.6 FERMAT 226 11.7 THE CASE N = 4 227 11.8 ODD PRIME EXPONENTS 228 11.9 LAME AND KUMMER 233 11.10 MODERN DEVELOPMENTS 234 11.11 FURTHER READING 237 APPENDIX A. INDUCTION AND WELL-ORDERING 239 APPENDIX B. GROUPS, RINGS AND FIELDS 243 APPENDIX C. CONVERGENCE 247 APPENDIX D. TABLE OF PRIMES P 1000 249 SOLUTIONS TO EXERCISES 251 BIBLIOGRAPHY 289 INDEX OF SYMBOLS 291 ELEMENTARY NUMBER THEORY INDEX OF NAMES 295 INDEX 297
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author	Jones, Gareth A. 1946- Jones, Josephine Mary 1946-
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dewey-raw	512/.7 512/.7 21
dewey-search	512/.7 512/.7 21
dewey-sort	3512 17
dewey-tens	510 - Mathematics
discipline	Mathematik
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spellingShingle	Jones, Gareth A. 1946- Jones, Josephine Mary 1946- Elementary number theory Number theory Zahlentheorie (DE-588)4067277-3 gnd
subject_GND	(DE-588)4067277-3 (DE-588)4123623-3
title	Elementary number theory
title_auth	Elementary number theory
title_exact_search	Elementary number theory
title_full	Elementary number theory Gareth A. Jones and J. Mary Jones
title_fullStr	Elementary number theory Gareth A. Jones and J. Mary Jones
title_full_unstemmed	Elementary number theory Gareth A. Jones and J. Mary Jones
title_short	Elementary number theory
title_sort	elementary number theory
topic	Number theory Zahlentheorie (DE-588)4067277-3 gnd
topic_facet	Number theory Zahlentheorie Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007888853&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT jonesgaretha elementarynumbertheory AT jonesjosephinemary elementarynumbertheory

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