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Free Download THE FUNDAMENTAL THEOREM OF ARITHMETIC: With an Elementary Introduction to Prime Numbers
English | July 10, 2025 | ASIN: B0FH9M8DJG | 235 pages | Epub | 9.90 MB
A prime number is a natural number greater than 1, which cannot be expressed as a product of two smaller natural numbers. Stated differently, a prime number is a number divided only by 1 and by itself. No other natural number can divide a prime number. For example, the numbers: 2, 3, 5, 7, 11, 13, 17, 19, etc, are prime numbers. All the other numbers are called composite numbers. For example, the numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, etc, are composite numbers. The prime number 7 is divided by 1 and 7 only, while the composite number 12 is divided by 1, by 12, but also, by 2, and by 3, and by 4, and by 6. Prime numbers, despite their simple definition, still hide many secrets, and their intensive study has been the subject of many eminent mathematicians, for more than 25 centuries. Prime numbers and their properties were studied, for the first time, by the ancient Greeks. Euclid defined a prime number as " a number measured by a unit alone " and also gave the first proof that there are infinitely many prime numbers, (around 300 BC). Eratosthenes of Cyrene, around 200 BC, devised a procedure, (an algorithm), to find all the prime numbers less than a given natural number, (the sieve of Eratosthenes). The main problem with prime numbers is that the way they appear is highly irregular. There is no known formula, or method, to predict the next prime number from the preceding one. Great mathematicians, Gauss, Euler and Riemann among others, have made important contributions to the prime numbers, but, the main problem of finding a pattern as how the prime numbers are distributed, still, remains unsolved. There are also, many other unsolved problems concerning the prime numbers. One of them is the Goldbach's conjecture , that every even number greater than 2 can be expressed as the sum of two primes. Another famous unsolved problem is the twin prime conjecture , that there are infinitely many pairs of primes that differ by 2, (like 3 and 5, 5 and 7, 11 and 13, 17 and 19, etc). Other unsolved problems concerning prime numbers and some historical remarks, like, Euclid's theorem, the sieve of Eratosthenes of Cyrene, Fermat numbers, etc, are discussed in section 3-4. Primes are of fundamental importance in number theory, because of the fundamental theorem of arithmetic: every natural number greater than 1, can be expressed as a product of prime numbers, and this product representation is unique . In this little book we provide a rigorous proof of this theorem and present some of its applications, (like for instance, to find the number of divisors and the sum of the divisors of any natural number, the perfect numbers and the amicable numbers). The material covered in the book is shown analytically in the table of contents. A comprehensive introduction to the prime numbers and some of its more important properties are presented, which are essential for the proof of the fundamental theorem. Solving problems with prime numbers is not an easy task. Most of the times, the solution requires ingenuity and imagination. Some other times, when a direct method of approach does not lead to the solution of the problem, we may proceed by contradiction, which is a popular and powerful method when working with prime numbers. The careful reader will find that many of the solved exercises have been solved by contradiction. The book contains 60 illustrative, solved exercises and 115 problems for solution.

Free Download THE EVERYDAY KETOGENIC FAVORITES: A Beginner's Keto Cookbook For Busy People with 100 Recipes And Ideas
English | July 15, 2019 | ASIN: B07VC43GNF | 155 pages | EPUB (True) | 3.32 MB
Are you looking for a way to lose weight,cook amazing meals that cater for the diverse needs of you and your family, shed that stubborn belly fat but don't know where to start? A ketogenic diet can be confusing for beginners, especially if you are a beginner who loves splurging on junk food. worry no more! In this cookbook, i will teach you how to not only start, but love, your hassle-free ketogenic diet, which will guide you to your weight loss goals in the most affordable, quick & easy way possible. Along the way, you'll learn to cook only the most high quality easy and ingredient ketogenic recipes, offering tons of scientifically proven health benefits, such as improving your appetite,stabilizing blood pressure cholesterol and reversing diabetes. Be rest assured, THE EVERYDAY KETOGENIC FAVORITES will get the healthy body you have always dreamt of! THE EVERYDAY KETOGENIC FAVORITES is the solution to lose weight, save time, and keep keto easy with ready-to-go meals from Monday-Saturdays. Little planning and preparation go a long way towards success on the ketogenic diet. THE EVERYDAY KETOGENIC FAVORITES has dozens of genius cooking hacks, with the low-carb, high-fat keto diet so you can have the flavor and texture you love while still ditching the pounds. It also include weight loss plan for people who love fluffy, crunchy, doughy, chewy, sweet foods. The cookbook makes it easy to keep keto on the table every day of the week with family-friendly, one-pot meals for your skillet, stock pot, slow cooker, sheet pan and more. With recipes ready to eat in under 30-50 minutes. Grab your copy today and start cooking amazing meals that cater for the diverse needs of you and your family, allowing you, the keto diet beginner, to save time, money and stress in the kitchen.

Free Download THE COLLAPSE OF NEWTON: 25 Irreversible Contradictions That End Gravity Forever
English | November 25, 2025 | ASIN: B0G3TWN4M8 | 477 pages | Epub | 580.24 KB
THE COLLAPSE OF NEWTON : 25 Irreversible Contradictions That End Gravity Forever -By Yashwant Kumar Messenger of Nature Raniganj, Imamganj, Gayaji, Bihar, India, 824210 November 25, 2025 Description: This book presents one of the most direct and uncompromising challenges ever posed to the idea of gravitational attraction. Instead of repeating traditional assumptions, it examines real physical behavior through clear examples, pressure mechanics, atmospheric behavior, density differences, orbital motion, and the universal rotation of celestial bodies. Every chapter exposes a contradiction that cannot be repaired within the framework of gravitational pull. The work begins with the fundamental observation that the universe is not made of empty space. There is no vacuum, no zero Kelvin region, and no place where particles are absent. This means that all motion occurs inside a filled medium where pressure gradients and density differences create push forces, not pull forces. Across the book, twenty-five powerful contradictions are explained with simple real-world examples: helium balloons that rise even when their mass increases, air rushing into tunnels from both ends, water hanging in a syringe until pressure is added, planetary drift toward the Sun as solar pressure weakens, the impossibility of straight-line geometry in a rotating universe, and many more. Each example shows that nature operates through pressure, temperature, and motion, not mass-based attraction. The book then builds a new foundation of physics based on pressure fields, rotational dynamics, and energy distribution. It explains how orbits form around moving low-pressure zones, how celestial bodies maintain their paths, and why push is the only fundamental mechanism the universe uses. Matter, motion, and energy are redefined in simple and observable terms. This is not a reinterpretation of old theories. It is a complete reconstruction of how the universe works, guided only by nature and direct observation. Scientists, students, and thinkers will find this book both challenging and eye-opening, as it questions every assumption that has been accepted for centuries. The Collapse of Newton is not just a book. It is an invitation to see the universe as it truly is: a filled, dynamic, pressure-driven cosmos where nothing pulls anything. It marks the beginning of a new understanding of physics and a new era of scientific thought.

Free Download TCL Programming with Tcl/Tk : A Practical Guide to Scripting, Testing, and GUI Development
English | November 7, 2025 | ASIN: B0G1CBRG7Q | 318 pages | EPUB (True) | 221.45 KB
Buried under brittle scripts that crash at runtime, GUIs that feel like 1990s relics, and endless debugging loops stealing your nights? You're desperate to harness Tcl/Tk for automation wizards, rock-solid testing frameworks, or sleek cross-platform interfaces, but cryptic errors, outdated examples, and zero real-world projects leave you stalled-promotions slipping, tools lagging, passion fading while others deploy elegant solutions effortlessly. It's infuriating: power at your fingertips, locked behind confusion.

Free Download Südafrika Kochbuch: 100 traditionelle Rezepte aus der südafrikanischen Küche von der Vorspeise bis zum Dessert - Inklusive Tipps zum Einkauf und vegane Rezepte
Deutsch | 1. Februar 2022 | ASIN: B09RMPZNQN | 220 Seiten | EPUB (True) | 10.43 MB
Sie wollen authentisches, südafrikanisches Essen zubereiten? Sie möchten wissen, was die südafrikanische Küche ausmacht? Dann ist dieses Kochbuch genau das Richtige für Sie! Bevor Sie sich gleich in die Küche stürzen, erwartet Sie eine Einleitung, in der Sie alles Wissenswertes über südafrikanisches Essen erfahren und zeitgleich Tipps und Tricks für die Zubereitung an die Hand bekommen. Direkt danach können Sie in 100 vielfältigen, leicht zuzubereitenden Rezepten stöbern. Egal, ob Sie eine Vorspeise, etwas zum Mittag- oder Abendessen, zum Frühstück oder ein süßes Dessert suchen - hier werden Sie das Richtige finden. Zudem finden Sie auch verschiedene Rezepte, falls Sie sich vegan ernähren. Die südafrikanische Küche ist unglaublich vielfältig, da in diesem Land viele unterschiedliche Einflüsse zusammenkommen. Guten Appetit!

THE FUNDAMENTAL THEOREM OF ARITHMETIC With an Elementary Introduction to Prime Numbers

THE EVERYDAY KETOGENIC FAVORITES A Beginner's Keto Cookbook For Busy People with 100 Recipes And Ideas

THE DIY COMPUTER REPAIR HANDBOOK Pratical step-by-step strategies For Diagnosing Faults, Servicing components, and Optimizing

THE COMPLETE INVERTER MINI SPLIT SYSTEM USER GUIDE Step-by-Step Instructions to Install, Operate & Troubleshoot Your Ductless

THE COLLAPSE OF NEWTON 25 Irreversible Contradictions That End Gravity Forever

THE ARCHITECT'S BLUEPRINT

TCL Programming with TclTk A Practical Guide to Scripting, Testing, and GUI Development

T-SQL from Scratch Become a Production SQL Server Administrator

T'Ai Chi Combat

Südafrika Kochbuch 100 traditionelle Rezepte aus der südafrikanischen Küche von der Vorspeise bis zum Dessert - Inklusive