Оглавление
Youri Veniaminovich Kraskov. The Wonders of Arithmetic from Pierre Simon de Fermat
Abstract
From the Author
Introduction
1. The Greatest Phenomenon of Science
2. The History of Delusions
3. What is a Number?
3.1. Definition the Notion of Number
3.2. Axioms of Arithmetic
3.2.1. Axioms of a Count
3.2.2. Axioms of Actions
3.2.3. Basic Properties of Numbers
3.3. The Basic Theorem of Arithmetic
3.3.1. Mistakes of the Greats and the Fermat's Letter-Testament
3.3.2. The Proof of Fermat
3.4. The Descent Method
3.4.1. A Little Bit of " Sharpness of Mind" for a Very Difficult Task
3.4.2. The Fermat’s Golden Theorem
3.4.3. Archimedes-Fermat Problem
3.4.4. Fermat’s Problem with Age 385 years
3.5. Parity Method
3.5.1. Defining Parity as a Number
3.5.2. Parity Law
3.5.3. Parity Calculation Rules
3.6. Key Formula Method
4. The Fermat’s Last Theorem
4.1. The Thorny Path to Truth
4.1.1. The FLT up to now remains unproven
4.1.2. Diophantus' Task
4.2. Fermat’s Proof
4.3. Theorems About Magic Numbers
4.4. Way of the FLT Proof Using the Parity Method
4.5. The Beal Theorem
4.6. The Theorems about the Wonders of Power Numbers’ Addition
5. Arithmetic Among Other Sciences
5.1. Ability to Think Abstractly
5.2. Comprehension of the Physical Essence
5.3. The Ghost Sciences
5.3.1. History
5.3.2. Informatics
5.3.3. Economics
6. Resume
6.1. New Approaches to Fundamentals of Science by Pierre Fermat
6.2. Methods of Problem Solving Based on the Essence the Notion of Number
6.3. Possibilities of Applying Scientific Approaches from Pierre Fermat in Physics
6.4. History as a Form of Existence All Branches of Knowledge
6.5. Informatics as the Science of Intangible Objects
6.6. Economy as a Way of Existence an Intelligent Civilization
APPENDICES
Appendix I
The Basic Theorem of Arithmetic
Zermelo Proof
Comments
Appendix II
FLT proof for n=4
Euler's proof
Fermat’s Proof
Comments
Appendix III
Fermat's theorems on primes of type 4n+1
Euler's Proofs
Comments
Appendix IV
HISTORICAL EPISODES
Year 1652 – Plague Epidemic
Year 1660 – Mysterious Newcomer
Year 1663 – Father and Son
Year 1680 – Family Council
Year 1908 – Mass Crazy
Year 2008 – Conversation of Two Lovely Gentlemen
Year 2020 – Games of School Girls
Appendix V
Unknown to Science Solutions of Problems and the Riddles Marked with (*)
Beginnings of Arithmetic
The Fermat’s Last Theorem
FLT proofs
Theorems about Magic Numbers
Beal Conjecture
Physics
History
Informatics
Economics
Hypotheses
Appendix VI
In memory of Pierre Fermat
Bibliography
The Complete List of Illustrations
