A Selection of Problems in the Theory of Numbers

A Selection of Problems in the Theory of Numbers

Popular Lectures in Mathematics

1st Edition - January 1, 1964

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  • Author: Waclaw Sierpinski
  • eBook ISBN: 9781483151465

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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.

Table of Contents


  • On the Borders of Geometry and Arithmetic

    What 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. Schinzel

    One Hundred Elementary but Difficult Problems in Arithmetic

    References


Product details

  • No. of pages: 126
  • Language: English
  • Copyright: © Pergamon 1964
  • Published: January 1, 1964
  • Imprint: Pergamon
  • eBook ISBN: 9781483151465

About the Author

Waclaw Sierpinski

About the Editors

I. N. Sneddon

M. Stark

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