Number theory with computer applications
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Upper Saddle River, NJ
Prentice-Hall
1998
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| 245 | 1 | 0 | |a Number theory with computer applications |c Ramanujachary Kumanduri ; Cristina Romero |
| 264 | 1 | |a Upper Saddle River, NJ |b Prentice-Hall |c 1998 | |
| 300 | |a XIII, 543 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1819621625121734656 |
|---|---|
| adam_text | NUMBER THEORY WITH COMPUTER APPLICATIONS RAMANUJACHARY KUMANDURI
DEPARTMENT OF MATHEMATICS COLUMBIA UNIVERSITY CRISTINA ROMERO PRENTICE
HALL UPPER SADDLE RIVER, NEW JERSEY 07458 CONTENTS PREFACE XI 1
INTRODUCTION 1 2 DIVISIBILITY AND PRIMES 7 2.1 DIVISIBILITY 7 2.2 PRIMES
15 2.3 UNIQUE FACTORIZATION 26 2.4 ELEMENTARY FACTORING METHODS 32 2.5
GCDANDLCM 38 2.6 LINEAR DIOPHANTINE EQUATIONS 48 3 MODULAR AERITHMETIC 59
3.1 CONGRUENCES 59 3.2 INVERSES MODULO M AND LINEAR CONGRUENCES 69 3.3
CHINESE REMAINDER THEOREM 73 3.4 POLYNOMIAL CONGRUENCES 81 3.5 MAGIC
SQUARES 88 4 FUNDAMENTAL THEOREMS OF MODULAR AERITHMETIC 103 4.1 FERMAT S
THEOREM 103 4.2 EULER S PHI FUNCTION 107 4.3 EULER S THEOREM 112 4.4
LAGRANGE S THEOREM 117 5 CRYPTOGRAPHY 121 5.1 CLASSICAL CRYPTOSYSTEMS
121 5.2 PUBLIC-KEY CRYPTOGRAPHY 131 5.3 THE RSA SCHEINE 137 6 PRIMALITY
TESTING AND FACTORING 145 6.1 PSEUDOPRIMES AND CARMICHAEL NUMBERS 145
6.2 STRENG PSEUDOPRIMES AND PREBABILISTIC PRIMALITY TESTING . . 150 6.3
POLLARD S (P - L)-METHOD 158 VII VIII CONTENTS 6.4 POLLARD S P-METHOD
162 7 PRIMITIVE ROOTS 169 7.1 THE CONCEPT OF ORDER 169 7.2 THE PRIMITIVE
ROOT THEOREM 176 7.3 THE DISCRETE LOGARITHM 182 7.4 PRIMALITY TESTING
186 8 APPLICATIONS 195 8.1 THE ELGAMAL SYSTEM 195 8.2 SIGNATURE SCHEMES
198 8.3 PSEUDORANDOM NUMBER GENERATORS-I 204 9 QUADRATIC CONGRUENCES 213
9.1 QUADRATIC RESIDUES 213 9.2 COMPUTING SQUARE ROOTS MOD P 223 9.3
COMPLETE SOLUTION OF QUADRATIC CONGRUENCES 230 10 APPLICATIONS 235 10.1
IDENTIFICATION SCHEMES 235 10.2 PSEUDORANDOM NUMBER GENERATORS-II 237 11
CONTINUED FRACTIONS 243 11.1 INTRODUCTION 243 11.2 CONVERGENTS 249 11.3
INFINITE CONTINUED FRACTIONS 257 11.4 QUADRATIC IRRATIONALS 264 11.5
PURELY PERIODIC CONTINUED FRACTIONS 270 11.6 CLASSICAL CONTINUED
FRACTION EXPANSIONS 273 12 FACTORING METHODS 285 12.1 CONTINUED FRACTION
FACTORING METHOD 285 12.2 QUADRATIC SIEVE 291 13 DIOPHANTINE
APPROXIMATIONS 297 13.1 BEST APPROXIMATIONS 297 13.2 INTERMEDIATE
CONVERGENTS AND GOOD APPROXIMATIONS .... 306 13.3 ALGEBRAIC AND
TRANSCENDENTAL NUMBERS 312 14 DIOPHANTINE EQUATIONS 319 14.1
INTRODUCTION 319 14.2 CONGRUENCE METHODS 323 14.3 PYTHAGOREAN TRIPLES
324 14.4 SUMS OF TWO SQUARES 331 CONTENTS IX 14.5 THE
BRAHMAGUPTA-BHASKARA EQUATION 340 14.6 FERMAT S LAST THEOREM 348 15
ARITHMETICAL FUNCTIONS AND DIRICHLET SERIES 357 15.1 ARITHMETICAL
FUNCTIONS 357 15.2 DIRICHLET SERIES 363 15.3 EULER PRODUCTS 368 15.4
MOEBIUS INVERSION FORMULA 375 15.5 DIRICHLET S THEOREM 380 16
DISTRIBUTION OF PRIMES 389 16.1 COUNTING PRIMES 389 16.2 CHEBYSHEV S
FUNCTIONS 392 16.3 CHEBYSHEV S THEOREM 397 16.4 THE RIEMANN ZETA
FUNCTION 404 17 QUADRATIC RECIPROCITY LAW 411 17.1 QUADRATIC RECIPROCITY
411 17.2 PROOF OF THE QUADRATIC RECIPROCITY LAW 421 17.3 THE JACOBI
SYMBOL 431 18 BINARY QUADRATIC FORMS 441 18.1 BASIC NOTIONS 441 18.2
REDUCTION OF DEFINITE FORMS-I 447 18.3 REDUCTION OF DEFINITE FORMS-II
453 18.4 GENUS THEORY 459 18.5 GENERIC CHARACTERS AND GENERA 462 18.6
THE NUMBER OF REPRESENTATIONS BY FORMS 471 19 ELLIPTIC CURVES 479 19.1
INTRODUCTION 479 19.2 PROJECTIVE SPACES 486 19.3 THE GROUP LAW ON
ELLIPTIC CURVES 491 19.4 ELLIPTIC CURVES MODULO PRIMES 498 19.5 RATIONAL
POINTS ON ELLIPTIC CURVES 503 19.6 ELLIPTIC CURVE FACTORIZATION METHOD
509 A MATHEMATICAL INDUCTION 513 B BINOMIAL THEOREM 519 C ALGORITHMIC
COMPLEXITY AND O-NOTATION 524 ANSWERS AND HINTS 527 X CONTENTS INDEX OF
NOTATION 535 INDEX 537
|
| any_adam_object | 1 |
| author | Kumanduri, Ramanujachary Romero, Cristina |
| author_facet | Kumanduri, Ramanujachary Romero, Cristina |
| author_role | aut aut |
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| bvnumber | BV011841209 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)36767980 (DE-599)BVBBV011841209 |
| dewey-full | 512/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.7 |
| dewey-search | 512/.7 |
| dewey-sort | 3512 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011841209 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T14:41:18Z |
| institution | BVB |
| isbn | 013801812X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007996967 |
| oclc_num | 36767980 |
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| owner_facet | DE-739 DE-355 DE-BY-UBR DE-19 DE-BY-UBM |
| physical | XIII, 543 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Prentice-Hall |
| record_format | marc |
| spellingShingle | Kumanduri, Ramanujachary Romero, Cristina Number theory with computer applications Nombre, théorie des - Informatique ram Nombre, théorie des ram Number theory Number theory Computer-assisted instruction Zahlentheorie (DE-588)4067277-3 gnd Computerarithmetik (DE-588)4135485-0 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4135485-0 |
| title | Number theory with computer applications |
| title_auth | Number theory with computer applications |
| title_exact_search | Number theory with computer applications |
| title_full | Number theory with computer applications Ramanujachary Kumanduri ; Cristina Romero |
| title_fullStr | Number theory with computer applications Ramanujachary Kumanduri ; Cristina Romero |
| title_full_unstemmed | Number theory with computer applications Ramanujachary Kumanduri ; Cristina Romero |
| title_short | Number theory with computer applications |
| title_sort | number theory with computer applications |
| topic | Nombre, théorie des - Informatique ram Nombre, théorie des ram Number theory Number theory Computer-assisted instruction Zahlentheorie (DE-588)4067277-3 gnd Computerarithmetik (DE-588)4135485-0 gnd |
| topic_facet | Nombre, théorie des - Informatique Nombre, théorie des Number theory Number theory Computer-assisted instruction Zahlentheorie Computerarithmetik |
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