Contents
Foreword: MASS and REU at Penn State University ix
Preface xi
Chapter 1. Arithmetic of the p-adic Numbers 1
§1.1. From Q to R; the concept of completion 2
Exercises 1-8 5
§1.2. Normed fields 6
Exercises 9-16 14
§1.3. Construction of the completion of a normed field 15
Exercises 17-19 19
§1.4. The field of p-adic numbers Qp 19
Exercises 20-25 26
§1.5. Arithmetical operations in Qp 27
Exercises 26-31 30
§1.6. The p-adic expansion of rational numbers 30
Exercises 32-34 33
§1.7. HenseFs Lemma and congruences 33
Exercises 35-44 38
§1.8. Algebraic properties of p-adic integers 39
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