Collection of Essays on Number Theory and Mathematical Conjectures: From Natural Number Structures to Unsolved Problems
This volume assembles a series of research papers in number theory published by Ramon Carbó-Dorca and some of his collaborators between 2023 and 2026. The collection focuses on several famous mathematical conjectures—the Collatz Conjecture, the (Strong) Goldbach Conjecture, Fermat’s Last Theorem, and the Riemann Hypothesis—and attempts to re-examine these classic problems from a unified perspective of “natural number vector structures.”
Sample Chapter(s)
Preface (139 KB)
Components of the Book:
  • Preface
  • Chapter 1. Whole Perfect Vectors and Fermat’s Last Theorem
  • Chapter 2. Heuristic Discussion on the Riemann Hypothesis
  • Chapter 3. Collatz Conjecture Redefinition on Prime Numbers
  • Chapter 4. Natural Numbers and the Strong Goldbach Conjecture
  • Chapter 5. On the Expression of Composite Natural Numbers as Tensorial Products of Prime Natural Powers Vectors
  • Chapter 6. Definition and Properties of a Vector-Matrix Reversal Operator
  • Chapter 7. Fermat Polynomials and Extended Fermat’s Theorem
  • Afterword
Readership: Students, academics, teachers and other people attending or interested in number theory and mathematical conjectures.
1
Preface
Ramon Carbó-Dorca
PDF (139 KB)
1
Chapter 1. Whole Perfect Vectors and Fermat’s Last Theorem
Ramon Carbó-Dorca
PDF (299 KB)
15
Chapter 2. Heuristic Discussion on the Riemann Hypothesis
Ramon Carbó-Dorca
PDF (695 KB)
27
Chapter 3. Collatz Conjecture Redefinition on Prime Numbers
Ramon Carbó-Dorca
PDF (371 KB)
45
Chapter 4. Natural Numbers and the Strong Goldbach Conjecture
Ramon Carbó-Dorca
PDF (474 KB)
93
Chapter 5. On the Expression of Composite Natural Numbers as Tensorial Products of Prime Natural Powers Vectors
Ramon Carbó-Dorca
PDF (244 KB)
107
Chapter 6. Definition and Properties of a Vector-Matrix Reversal Operator
Ramon Carbó-Dorca
PDF (352 KB)
123
Chapter 7. Fermat Polynomials and Extended Fermat’s Theorem
Ramon Carbó-Dorca
PDF (355 KB)
147
Afterword
Ramon Carbó-Dorca
PDF (141 KB)
Ramon Carbó-Dorca
Ramon Carbó-Dorca (born on October 19, 1940, in Girona, Catalonia, Spain) is a chemical engineer and chemist. His academic career has been primarily centred in Barcelona. He obtained a Bachelor's degree (1964) and a PhD (1968) in Chemical Engineering from the Institut Químic de Sarrià (IQS). Subsequently, he earned two further degrees in Chemistry: a Bachelor's from the Universitat de Barcelona (1970) and a PhD from the Universitat Autònoma de Barcelona (UAB) (1974).

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