Elementary Theory Of NumbersWorld Scientific Publishing Company, 20. okt. 1992 - 260 strani This book explains clearly and in detail the basic concepts and methods of calculations of the elementary theory of numbers. It consists of 7 chapters illustrated by numerous examples and exercises. Answers together with some hints to the exercises are given at the end of the book. It may be used as a textbook for undergraduate students. |
Vsebina
1 | |
Chapter 2 CONGRUENCES | 51 |
Chapter 3 INDETERMINATE EQUATIONS | 77 |
Chapter 4CONGRUENCE IN ONE UNKNOWN | 109 |
Chapter 5 QUADRATIC RESIDUES AND CONGRUENCES OF SECOND DEGREE IN ONE UNKNOWN | 139 |
Chapter 6 PRIMITIVE ROOTS AND INDEX | 181 |
Chapter 7 BRIEF INTRODUCTION TO NUMBER THEORY | 207 |
APPENDIX | 219 |
ANSWERS TO EXERCISES | 223 |
249 | |
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algebraic integer algebraic number theory called complete residue system completes the proof computation congruent modulo conjecture Conversely cºq different solutions digits discuss divided Euler Evidently Exercise exist Fermat number following theorem form 4n Gauss given congruence given equation greatest common divisor Hence the theorem incongruent modulo indeterminate equation infinitely Jacobi symbol least common multiple least positive Legendre symbol Mersenne numbers method mod m2 mod q necessary and sufficient number of integers number of solutions obtain odd integer odd number odd prime factors perfect number positive divisors positive integer solution prime divisor prime number primitive root problem quadratic nonresidue quadratic residue real number reduced residue system relatively prime required solution residue system modulo second degree Show Similarly solutions of f(z solving the congruence square number sufficient condition system of congruences theorem is proved Wilson's theorem