Mathematical Marvels First Steps in Number Theory A Primer on Divisibility by Shailesh Shirali Universities Press RMO INMO MathematICS Olympiad IMO.pdf
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Universities Press MATHEMATICS Mathematical Marvels FIRST STEPS IN NUMBER THEORY A Primer on DIVISIBILITY 3200023 0000000000 4 6 5 0 00000 0000000000000000 Shailesh Shirali Mathematical Marvels FIRST STEPS IN NUMBER THEORY A Primer on DIVISIBILITY Shailesh Shirali ur Universities Press Contents Preface vii 1 Introduction 1 1.1 What Is Number Theory? 1 1.2 Terms And Symbols 5 2 Congruences 9 2.1 Introduction 9 2.2 Odd And Even Numbers 9 2.3 The Remainder Symbol 11 2.4 Other Divisors 12 2.5 The Congruence Symbol 14 2.6 Using Congruences 20 2.7 A Test For Divisibility By 13 21 2.8 Using Negative Remainders 23 3 The Elementary Cases 25 3.1 Introduction 25 3.2 Divisibility By 2 25 3.3 Divisibility By 5 29 3.4 Divisibility By 4 29 3.5 A Generalization 31 4 The Remaining Cases 34 4.1 Introduction 34 4.2 Divisibility By 9 34 4.3 Divisibility By 11 37 4.4 More General Results 42 4.5 Divisibility By 101 43 4.6 Divisibility By 7 And 13 44 4.7 Divisibility By 27 And 37 46 4.8 Other Divisors 47 4.9 Concluding Remarks 49 52 5 A Different Approach 52 5.1 Introduction ...