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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