Number theory: step by step
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2020
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| Edition: | First edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xi, 385 Seiten Illustrationen |
| ISBN: | 9780198846734 |
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Record in the Search Index
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| adam_text | Contents Introduction to Number Theory Step by Step ix 1 A Survey of Divisibility 1.1 1.2 1.3 1.4 2 Primes and Factorization 2.1 2.2 2.3 2.4 3 5 6 1 11 18 30 42 45 Introduction to Primes Testing Numbers for Primality Properties of Prime Numbers Least Common Multiple-LCM Supplementary Problems 2 45 54 64 77 88 Theory of Modular Arithmetic 91 3.1 3.2 3.3 3.4 3.5 4 The Greatest Common Divisor Division Algorithm Euclidean Algorithm Linear Diophantine Equations Supplementary Problems 1 1 Introduction to Congruences Congruent Properties of Multiplication Solving Linear Congruences Chinese Remainder Theorem Introduction to Factorization Supplementary Problems 3 91 111 118 130 141 151 A Survey of Modular Arithmetic with Prime Moduli 153 4.1 4.2 4.3 4.4 4.5 153 163 171 182 195 206 Introduction to Fermat s Little Theorem Wilson s Theorem Composite Integers and Pseudoprimes (False Primes) Mersenne Numbers Perfect Numbers and the SigmaFunction Supplementary Problems 4 Euler s Generalization of Fermat s Theorem 209 5.1 5.2 Euler s Totient Function Euler s Theorem Supplementary Problems 5 209 223 233 Primitive Roots and Indices 235 6.1 6.2 6.3 6.4 6.5 The Order of an Integer modulo n Indices Theory of Indices Integers with Primitive Roots Composite Integers with PrimitiveRoots - Companion Website Supplementary Problems 6 235 246 254 267 275
CONTENTS 7 8 Quadratic Residues 277 7.1 12 7.3 7.4 7.5 Til 290 301 315 Introduction to Quadratic Residues The Legendre Symbol Quadratic Reciprocity Law of Quadratic Reciprocity (LQR) Quadratic Residues of CompositeModuli Companion Website Supplementary Problems 7 328 Non-Linear Diophantine Equations 331 8.1 8.2 8.3 331 344 353 365 Sum of Two Squares Sum of Four Squares Pell s Equation Supplementary Problems 8 introductory Chapter Companion Website Brief Solutions 369 Symbolic Index 383 Index 384
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| illustrated | Illustrated |
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| institution | BVB |
| isbn | 9780198846734 |
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| publisher | Oxford University Press |
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| spelling | Singh, Kuldeep Verfasser (DE-588)1047476231 aut Number theory step by step Kuldeep Singh First edition Oxford Oxford University Press 2020 xi, 385 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031862964&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Singh, Kuldeep Number theory step by step Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 |
| title | Number theory step by step |
| title_auth | Number theory step by step |
| title_exact_search | Number theory step by step |
| title_full | Number theory step by step Kuldeep Singh |
| title_fullStr | Number theory step by step Kuldeep Singh |
| title_full_unstemmed | Number theory step by step Kuldeep Singh |
| title_short | Number theory |
| title_sort | number theory step by step |
| title_sub | step by step |
| topic | Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031862964&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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