## Elements of Number Theory"A very welcome addition to books on number theory."— Bulletin, American Mathematical SocietyClear and detailed in its exposition, this text can be understood by readers with no background in advanced mathematics; only a small part requires a working knowledge of calculus. One of the most valuable characteristics of this book is its stress on learning number theory by means of demonstrations and problems. More than 200 problems and full solutions appear in the text, plus 100 numerical exercises. Some of these exercises deal with estimation of trigonometric sums and are especially valuable as introductions to more advanced studies. Translation of 1949 Russian edition. |

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### Contents

Common Divisor 2 3 The Least Common Multiple | 7 |

composition 15 Problems for Chapter I 17 Numerical | 20 |

4 The Euler Function 26 Problems for Chapter II 28 | 40 |

Chapter IV | 59 |

lus 65 5 Congruences of Arbitrary Degree with Com | 77 |

3 The Jacobi Symbol 87 4 The Case of Composite | 103 |

pa and 2pa 106 3 Evaluation of Primitive Roots for | 113 |

6 Indices Modulo 2a 116 7 Indices for Arbitrary Com | 130 |

Solutions for Chapter I 133 Solutions for Chapter II 139 | 139 |

Solutions for Chapter III 161 Solutions for Chapter IV 178 | 178 |

Solutions for Chapter V 187 Solutions for Chapter VI 202 | 202 |

Answers for Chapter I 217 Answers for Chapter II 217 | 217 |

226 | |

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### Common terms and phrases

apply the theorem canonical decomposition complete residue system condition congruence x2 continued fraction cp(a cp(m deduce divides divisible equal Example exp 2ni exponent Farey series follows form 4m formula function 6(a greatest common divisor gruence hence incongruent modulo infinite number Jacobi symbol lattice points least common multiple least non-negative residues Legendre symbol let the function let x run Mmod mod ml multiplicative function number of integers number of lattice number of primes number of solutions number of values obtain the required odd prime positive integers prime divisors prime numbers primitive root modulo problem 17 Problems for Chapter quadratic non-residue quadratic residue real numbers reduced residue system relatively prime residue system modulo residues modulo right side rm(a sequence smallest solvable Solve the congruence symbol system of residues system x theorem of problem x0 mod

### References to this book

Classical and Quantum Computation Alexei Yu. Kitaev,Alexander Shen,Mikhail N. Vyalyi No preview available - 2002 |