Number Theory Explorations: A Collection of Mathematical Papers

This volume brings together a series of mathematical papers that explore diverse topics in number theory, abstract algebra, and combinatorial mathematics. The works presented here, originally published in Advances in Pure Mathematics between 2016 and 2024, represent significant contributions to their respective fields while maintaining accessibility to mathematically inclined readers.

Sample Chapter(s)
Preface (58 KB)

Components of the Book:

Chapter 1. On Irrational Points in the Plane

Chapter 2. Pringsheim Convergence and the Dirichlet Function

Chapter 3. Factorization Patterns in F_q[x}

Chapter 4. Small Modular Solutions to Fermat’s Last Theorem

Chapter 5. Generalized Series of Bernoulli Type

Chapter 6. A Geometric Proof of Fermat’s Little Theorem

Chapter 7. On Conditional Probabilities of Factoring Quadratics

Afterword

Readership: Students, academics, teachers, and other people attending or interested in Math.

1		Chapter 1. On Irrational Points in the Plane Thomas Beatty PDF (165 KB)

11		Chapter 2. Pringsheim Convergence and the Dirichlet Function Thomas Beatty PDF (192 KB)

21		Chapter 3. Factorization Patterns in F_q[x} Thomas Beatty PDF (226 KB)

		Chapter 4. Small Modular Solutions to Fermat’s Last Theorem Thomas Beatty PDF (226 KB)

49		Chapter 5. Generalized Series of Bernoulli Type Thomas Beatty PDF (197 KB)

59		Chapter 6. A Geometric Proof of Fermat’s Little Theorem Thomas Beatty PDF (145 KB)

65		Chapter 7. On Conditional Probabilities of Factoring Quadratics Thomas Beatty PDF (575 KB)

81		Afterword Thomas Beatty PDF (128 KB)