A Selection of Problems in the Theory of Numbers
Popular Lectures in Mathematics
Published on 16. May 2014
126 pages
978-1-4831-5146-5 (ISBN)
Description
A Selection of Problems in the Theory of Numbers focuses on mathematical problems within the boundaries of geometry and arithmetic, including an introduction to prime numbers. This book discusses the conjecture of Goldbach; hypothesis of Gilbreath; decomposition of a natural number into prime factors; simple theorem of Fermat; and Lagrange's theorem. The decomposition of a prime number into the sum of two squares; quadratic residues; Mersenne numbers; solution of equations in prime numbers; and magic squares formed from prime numbers are also elaborated in this text. This publication is a good reference for students majoring in mathematics, specifically on arithmetic and geometry.
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Waclaw Sierpinski
Selection of Problems in the Theory of Numbers
Book
12/1964
Pergamon
€2.42
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Content
On the Borders of Geometry and ArithmeticWhat We Know and What We Do Not Know about Prime Numbers 1. What are Prime Numbers? 2. Prime Divisors of a Natural Number 3. How Many Prime Numbers are There? 4. How to Find All the Primes Less than a Given Number 5. Twin Primes 6. Conjecture of Goldbach 7. Hypothesis of Gilbreath 8. Decomposition of a Natural Number into Prime Factors 9. Which Digits Can There Be at the Beginning and at the End of a Prime Number? 10. Number of Primes Not Greater than a Given Number 11. Some Properties of the n-th Prime Number 12. Polynomials and Prime Numbers 13. Arithmetic Progressions Consisting of Prime Numbers 14. Simple Theorem of Fermat 15. Proof That There is an Infinity of Primes in the Sequences 4k+1, 4k+3 and 6k+5 16. Some Hypotheses about Prime Numbers 17. Lagrange's Theorem 18. Wilson's Theorem 19. Decomposition of a Prime Number into the Sum of Two Squares 20. Decomposition of a Prime Number into the Difference of Two Squares and Other Decompositions 21. Quadratic Residues 22. Fermat Numbers 23. Prime Numbers of the Form nn + 1, nnn + 1 etc. 24. Three False Propositions of Fermat 25. Mersenne Numbers 26. Prime Numbers in Several Infinite Sequences 27. Solution of Equations in Prime Numbers 28. Magic Squares Formed from Prime Numbers 29. Hypothesis of A. SchinzelOne Hundred Elementary but Difficult Problems in ArithmeticReferences
