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Unsolved problems in number theory

Author: Richard K Guy
Publisher: New York, NY : Springer, 2005.
Series: Problem books in mathematics
Edition/Format:   Print book : English : 3. ed., 2. [print.]View all editions and formats
Summary:

Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Richard K Guy
ISBN: 0387208607 9780387208602
OCLC Number: 634701581
Description: XVIII, 437 Seiten : Diagramme.
Contents: Preface to the First EditionPreface to the Second EditionPreface to the Third EditionGlossary of SymbolsA. Prime Numbers.A1. Prime values of quadratic functions.A2. Primes connected with factorials.A3. Mersenne primes. Repunits. Fermat numbers. Primes of shape k * 2n + 1. A4. The prime number race.A5. Arithmetic progressions of primes.A6. Consecutive primes in A.P. A7. Cunningham chains.A8. Gaps between primes. Twin primes. A9. Patterns of primes.A10. Gilbreath's conjecture.A11. Increasing and decreasing gaps.A12. Pseudoprimes. Euler pseudoprimes. Strong pseudoprimes. A13. Carmichael numbers.A14. 'Good' primes and the prime number graph.A15. Congruent products of consecutive numbers. A16. Gaussian primes. Eisenstein-Jacobi primes. A17. Formulas for primes. A18. The Erd1/2os-Selfridge classi.cation of primes. A19. Values of n making n - 2k prime. Odd numbers not of the form +/-pa +/- 2b. A20. Symmetric and asymmetric primes. B. Divisibility B1. Perfect numbers. B2. Almost perfect, quasi-perfect, pseudoperfect, harmonic, weird, multiperfect and hyperperfect numbers. B3. Unitary perfect numbers. B4. Amicable numbers. B5. Quasi-amicable or betrothed numbers. B6. Aliquot sequences. B7. Aliquot cycles. Sociable numbers. B8. Unitary aliquot sequences. B9. Superperfect numbers. B10. Untouchable numbers. B11. Solutions of mo(m) = no(n). B12. Analogs with d(n), ok(n). B13. Solutions of o(n) = o(n + 1). B14. Some irrational series. B15. Solutions of o(q) + o(r) = o(q + r). B16. Powerful numbers. Squarefree numbers. B17. Exponential-perfect numbers B18. Solutions of d(n) = d(n + 1). B19. (m, n + 1) and (m+1, n) with same set of prime factors. The abc-conjecture. B20. Cullen and Woodallnumbers. B21. k * 2n + 1 composite for all n. B22. Factorial n as the product of n large factors. B23. Equal products of factorials. B24. The largest set with no member dividing two others. B25. Equal sums of geometric progressions with prime ratios. B26. Densest set with no l pairwise coprime. B27. The number of prime factors of n + k which don't divide n + i, 0 !UE i < k.B28. Consecutive numbers with distinct prime factors. B29. Is x determined by the prime divisors of x + 1, x + 2,. . ., x + k? B30. A small set whose product is square. B31. Binomial coeffcients. B32. Grimm's conjecture. B33. Largest divisor of a binomial coeffcient. B34. If there's an i such that n - i divides _nk_. B35. Products of consecutive numbers with the same prime factors. B36. Euler's totient function. B37. Does oe(n) properly divide n - 1? B38. Solutions of oe(m) = o(n). B39. Carmichael's conjecture. B40. Gaps between totatives. B41. Iterations of oe and o. B42. Behavior of oe(o(n)) and o(oe(n)). B43. Alternating sums of factorials. B44. Sums of factorials. B45. Euler numbers. B46. The largest prime factor of n. B47. When does 2a -2b divide na - nb? B48. Products taken over primes. B49. Smith numbers. C. Additive Number Theory C1. Goldbach's conjecture. C2. Sums of consecutive primes. C3. Lucky numbers. C4. Ulam numbers. C5. Sums determining members of a set. C6. Addition chains. Brauer chains. Hansen chains. C7. The money-changing problem. C8. Sets with distinct sums of subsets. C9. Packing sums of pairs. C10. Modular di.erence sets and error correcting codes. C11. Three-subsets with distinct sums. C12. The postage stamp problem. C13. The corresponding modular covering problem. Harmonious labelling of graphs. C14.
Series Title: Problem books in mathematics
Responsibility: Richard K. Guy.

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From the reviews of the third edition: "This is the third edition of Richard Guy's well-known problem book on number theory ... . The earlier editions have served well in providing beginners as well Read more...

 
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