A selection of problems in the theory of numbers
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 factor...
| Main Author: | Sierpinski, Waclaw, 1882-1969, |
|---|---|
| Other Authors: | Sharma, A., ScienceDirect (Online service) |
| Format: | eBook |
| Language: | English Polish |
| Published: |
Oxford : Warszawa :
Pergamon Press ; PWN -- Polish Scientific Publishers,
1964.
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| Physical Description: |
1 online resource. |
| Series: |
Popular lectures in mathematics (New York, N.Y.) ;
Volume 11. |
| Subjects: |
Table of Contents:
- Front Cover; A Selection of Problems in the Theory of Numbers; Copyright Page; Table of Contents; Acknowledgement; Chapter 1. ON THE BORDERS OF GEOMETRY AND ARITHMETIC; Chapter 2. 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 nth 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 decompositions21. Quadratic residues; 22. Fermat numbers; 23. Prime numbers of the form nn+l, 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; Chapter 3. ONE HUNDRED ELEMENTARY BUT DIFFICULT PROBLEMS IN ARITHMETIC; REFERENCES.