圖書目錄 Preface 16 Mathematical Induction 17 Arithmetic Progressions and Geometric Progressions 18 Recursive Sequences 19 Summation of Various Sequences 20 Some Fundamental Theorems on Congruence 21 Chinese Remainder Theorem and Order of Integer 22 Diophantine Equations (III) 23 Pythagorean Triples and Pell's Equations 24 Quadratic Residues 25 Some Important Inequalities (I) 26 Some Important Inequalities (II) 27 Some Methods for Solving Inequalities 28 Some Basic Methods in Counting (I) 29 Some Basic Methods in Counting (II) 30 Introduction to Functional Equations Solutions to Testing Questions Appendices A Theorem on Second Order Recursive Sequences B Proofs of Theorems on Pell's Equation C Theorems on Quadratic Residues D Proofs of Some Important Inequalities E Note on Cauchy's Problem in Functional Equations Index