Elementary Theory of Numbers: Second English Edition (edited by A. Schinzel)Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised.The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of Gaussian integers. |
Contents
| 1 | |
| 32 | |
Chapter III Prime Numbers | 113 |
Chapter IV Number of Divisors and Their Sum | 166 |
Chapter V Congruences | 198 |
Chapter VI EulerS Totient Function and The Theorem of Euler | 245 |
Chapter VII Representation of Numbers Bydecimals in a Given Scale | 285 |
Chapter VIII Continued Fractions | 304 |
Chapter X Mersenne Numbers and Fermat Numbers | 360 |
Chapter XI Representations of Natural Numbers as Sums of Non negative kth Powers | 378 |
Chapter XII Some Problems of the Additive Theory of Numbers | 431 |
Chapter XIII Complex Integers | 449 |
Bibliography | 482 |
| 505 | |
| 511 | |
Addendum and Corrigendum Inserted in July 1987 | 514 |
Common terms and phrases
a₁ arbitrary natural number arithmetical progression b₁ c₁ complex integers composite number congruence Conjecture H Consequently COROLLARY cubes d₁ denote digits Diophantine equation divisible easy to prove equal equation x² exist infinitely exist natural numbers exponent fact Fermat form 4k formula given natural number greatest common divisor Hence implies inequality infinitely many natural infinitely many primes least natural number lemma m₁ magic square Math modulus n₁ number greater number n numbers a1 obtain odd natural number odd number odd prime P₁ pairs polynomial prime divisor prime factors prime numbers primitive root pseudoprime Pythagorean triangles quadratic residue rational numbers real number relatively prime representation Schinzel sequence Sierpiński simple continued fraction solution of equation solutions in natural sum of four summands super-Poulet Suppose Theorem 13 virtue whence x₁