Contents

Foreword xi

Notation xiii

Acknowledgements xiv

Chapter 1. Elementary Prime Number Theory, I 1

§1. Introduction 1

§2. Euclid and his imitators 2

§3. Coprime integer sequences 3

§4. The Euler-Riemann zeta function 4

§5. Squarefree and smooth numbers 9

§6. Sledgehammers! 12

§7. Prime-producing formulas 13

§8. Euler’s prime-producing polynomial 14

§9. Primes represented by general polynomials 22

§10. Primes and composites in other sequences 29

Notes 32

Exercises 34

Chapter 2. Cyclotomy 45

§1. Introduction 45

§2. An algebraic criterion for constructibility 50

§3. Much ado about Z[ζp] 52

§4. Completion of the proof of the Gauss–Wantzel theorem 55

§5. Period polynomials and Kummer’s criterion 57

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