In this post, we will see the book A Collection of Problems in The Theory of Numbers by Waclaw Sierpinski.
About the book
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.
The book was translated from Polish by A. Sharma and was published in 1964.
Credits to original uploader.
You can get the book here.
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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