Exploring, Investigating and Discovering in Mathematics

Preface Introduction.- 1 Chase problems.- 2 Sequences of Integers Simultaneously Prime.- 3 A Geometric Construction Using Ruler and Compass.- 4 Solving a Class of Nonlinear Systems.- 5 A Class of Homogenous Inequalities.- 6 The First Decimal of Some Irrational Numbers.- 7 Polynomial Approximation of Continuous Functions.- 8 On an Interesting Divisibility Problem.- 9 Determinants with Alternate Entries.- 10 Solving Some Cyclic Systems.- 11 On a Property of Recurrent Affine Sequences.- 12 Binomial Characterizations of Arithmetic Progressions.- 13 Using Duality in Studying Homographic Recurrences.- 14 Exponential Equations Having Exactly Two Solutions.- 15 A Class of Functional Equations.- 16 An Extension of the Leibniz-Newton Formula.- 17 A Measurement Problem.- 18 A Class of Discontinuous Functions Admitting Primitives.- 19 On Two Classes of Inequalities.- 20 Another Problem of Geometric Construction.- 21 How Can We Discover New Problems by Means of the Computer.- 22 On the Convergence of Some Sequences of Real Numbers.- 23 An Application of the Integral Mean.- 24 Difference and Differential Equations.- Addendum.