Elementary Number Theory with ApplicationsAcademic Press, 2002 - Всего страниц: 716 Elementary Number Theory focuses on number theory's role in the rapid development of art, coding theory, cryptology, computer science, and other necessities of modern life - confirming that human ingenuity and creativity are boundless. |
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Стр. vii
... Exercises Computer Exercises Enrichment Readings xi M xvii 1 3 9 16 27 33 41 50 54 56 58 61 62 2 Divisibility Theory 3 2.1 The Division Algorithm * 2.2 Base - b Representations ( optional ) . * 2.3 Operations in Nondecimal Bases ...
... Exercises Computer Exercises Enrichment Readings xi M xvii 1 3 9 16 27 33 41 50 54 56 58 61 62 2 Divisibility Theory 3 2.1 The Division Algorithm * 2.2 Base - b Representations ( optional ) . * 2.3 Operations in Nondecimal Bases ...
Стр. viii
... Exercises . . Supplementary Exercises Computer Exercises . 167 170 180 184 186 188 189 189 Enrichment Readings 4 Linear Diophantine Equations and Congruences 191 4.1 Linear Diophantine Equations ... 191 * 4.2 Linear Diophantine ...
... Exercises . . Supplementary Exercises Computer Exercises . 167 170 180 184 186 188 189 189 Enrichment Readings 4 Linear Diophantine Equations and Congruences 191 4.1 Linear Diophantine Equations ... 191 * 4.2 Linear Diophantine ...
Стр. ix
... Exercises . . Supplementary Exercises Computer Exercises .. Enrichment Readings Multiplicative Functions ... 8.1 Euler's Phi Function Revisited . 311 311 316 325 328 336 337 339 340 341 343 343 8.2 The Tau and Sigma Functions . 353 ...
... Exercises . . Supplementary Exercises Computer Exercises .. Enrichment Readings Multiplicative Functions ... 8.1 Euler's Phi Function Revisited . 311 311 316 325 328 336 337 339 340 341 343 343 8.2 The Tau and Sigma Functions . 353 ...
Стр. x
... Exercises .. Supplementary Exercises Computer Exercises Enrichment Readings 12 Nonlinear Diophantine Equations . 12.1 Pythagorean Triples ... 12.2 Fermat's Last Theorem .. 12.3 Sums of Squares . 12.4 Pell's Equation .. Chapter Summary ...
... Exercises .. Supplementary Exercises Computer Exercises Enrichment Readings 12 Nonlinear Diophantine Equations . 12.1 Pythagorean Triples ... 12.2 Fermat's Last Theorem .. 12.3 Sums of Squares . 12.4 Pell's Equation .. Chapter Summary ...
Стр. xii
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Содержание
27 | 68 |
Linear Diophantine Equations and Congruences | 191 |
Congruence Applications | 243 |
Systems of Linear Congruences | 287 |
Chapter Summary | 311 |
Quadratic Congruences | 374 |
252 | 380 |
Computer Exercises | 394 |
Canonical Decompositions | 537 |
Appendix | 583 |
Web Sites | 591 |
271 | 597 |
483 | 599 |
10 | 603 |
Least Primitive Roots Modulo Primes | 607 |
Solutions to OddNumbered Exercises | 619 |
257 | 395 |
Chapter Summary | 472 |
267 | 508 |
Nonlinear Diophantine Equations | 533 |
161 | 632 |
Credits | 705 |
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Часто встречающиеся слова и выражения
affine cipher canonical decomposition check digit Chinese Remainder Theorem ciphertext composite number compute congruence x2 conjecture contradiction Corollary deciphering denote the number Determine digital root distinct primes divisor encryption Euler's criterion Exercise Fermat number Fermat's little theorem Figure Find the number following example illustrates following theorem formula Gauss incongruent solutions induction inverse law of quadratic least positive least residues modulo Legendre symbol Lemma linear congruence linear diophantine equation linear system mathematician Mersenne number Mersenne primes mod 9 multiplicative number of positive number theory odd integer odd prime ordm perfect number perfect square plaintext positive integer prime factor prime numbers primitive Pythagorean triple primitive root modulo Prove pseudoprime Pythagorean triangle Pythagorean triple quadratic nonresidue quadratic reciprocity quadratic residue recursively relatively prime result shows solution of x² solvable Solve Suppose Table unique solution Verify yields