Unsolved problems in number theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1994
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Unsolved problems in intuitive mathematics
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 285 S. graph. Darst. |
| ISBN: | 3540942890 0387942890 |
Internformat
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| 245 | 1 | 0 | |a Unsolved problems in number theory |c Richard K. Guy |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York u.a. |b Springer |c 1994 | |
| 300 | |a XVI, 285 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Unsolved problems in intuitive mathematics |v 1 | |
| 490 | 0 | |a Problem books in mathematics | |
| 650 | 7 | |a Getaltheorie |2 gtt | |
| 650 | 4 | |a Nombres, Théorie des | |
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| 650 | 4 | |a Number theory | |
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Datensatz im Suchindex
| _version_ | 1804123998252957696 |
|---|---|
| adam_text | Contents
Preface to the First Edition v
Preface to the Second Edition vii
Glossary of Symbols xiii
Introduction 1
A. Prime Numbers 3
Al. Prime values of quadratic functions. 4 A2. Primes connected with
factorials. 7 A3. Mersenne primes. Repunits. Fermat
numbers. Primes of shape k ¦ 2n + 2. 8 A4. The prime number race. 13
A5. Arithmetic progressions of primes. 15 A6. Consecutive primes in
A.P. 17 A7. Cunningham chains. 18 A8. Gaps between primes.
Twin primes. 19 A9. Patterns of primes. 23 A10. Gilbreath s
conjecture. 25 All. Increasing and decreasing gaps. 26
A12. Pseudoprimes. Euler pseudoprimes. Strong pseudoprimes. 26
A13. Carmichael numbers. 30 A14. Good primes and the prime
number graph. 32 A15. Congruent products of consecutive numbers. 33
A16. Gaussian primes. Eisenstein Jacobi primes. 33 A17. Formulas for
primes. 36 A18. The Erdos Selfridge classification of primes. 41
A19. Values of n making n 2k prime. Odd numbers not of the form
±pa ± 2b. 42
B. Divisibility 44
Bl. Perfect numbers. 44 B2. Almost perfect, quasi perfect,
pseudoperfect, harmonic, weird, multiperfect and hyperperfect
numbers. ^5 B3. Unitary perfect numbers. 53 B4. Amicable
numbers. 55 B5. Quasi amicable or betrothed numbers. 59
B6. Aliquot sequences. 60 B7. Aliquot cycles or sociable numbers. 62
B8. Unitary aliquot sequences. 63 B9. Superperfect numbers. 65
BlO. Untouchable numbers. 66 Bll. Solutions of ma(m) = na(n). 67
B12. Analogs with d(n), ak{n). 61 B13. Solutions of
a{n) = a(n + 1). 68 B14. Some irrational series. 69 B15. Solutions
ix
x Contents
of a(q) + air) = a(q + r). 69 B16. Powerful numbers. 10
B17. Exponential perfect numbers. 13 B18. Solutions of
d(n) = d[n + 1). 13 B19. (m,n + 1) and (m + l,n) with same set of
prime factors. 15 B20. Cullen numbers. 11 B21. k ¦ 2n + 1 composite
for all n. 11 B22. Factorial n as the product of n large factors. 19
B23. Equal products of factorials. 19 B24. The largest set with no
member dividing two others. 80 B25. Equal sums of geometic
progressions with prime ratios. 81 B26. Densest set with no I pairwise
coprime. 81 B27. The number of prime factors of n + k which don t
divide n + i, 0 i k. 82 B28. Consecutive numbers with distinct
prime factors. 83 B29. Is x determined by the prime divisors of x + 1,
x + 2, ..., x + k? 83 B30. A small set whose product is square. 84
B31. Binomial coefficients. 84 B32. Grimm s conjecture. 85
B33. Largest divisor of a binomial coefficient. 81 B34. If there s an i
such that n — i divides (£). 89 B35. Products of consecutive numbers
with the same prime factors. 89 B36. Euler s totient function. 90
B37. Does (f {n) properly divide n 1? 92 B38. Solutions of
(fr(m) = a(n). 93 B39. Carmichael s conjecture. 94 B40. Gaps
between totatives. 95 B41. Iterations of (p and a. 96 B42. Behavior
of (j (a(n)) and a(4 (n)). 99 B43. Alternating sums of factorials. 99
B44. Sums of factorials. 100 B45. Euler numbers. 101 B46. The
largest prime factor of n. 101 B47. When does 2a 2b divide
n° n6? 102 B48. Products taken over primes. 102 B49. Smith
numbers. 103
C. Additive Number Theory 105
Cl. Goldbach s conjecture. 105 C2. Sums of consecutive primes. 101
C3. Lucky numbers. 108 C4. Ulam numbers. 109 C5. Sums
determining members of a set. 110 C6. Addition chains. Brauer chains.
Hansen chains. Ill C7. The money changing problem. 113 C8. Sets
with distinct sums of subsets. 114 C9. Packing sums of pairs. 115
CIO. Modular difference sets and error correcting codes. 118
Cll. Three subsets with distinct sums. 121 C12. The postage stamp
problem. 123 C13. The corresponding modular covering problem.
Harmonious labelling of graphs. 121 C14. Maximal sum free sets. 128
C15. Maximal zero sum free sets. 129 C16. Nonaveraging sets.
Nondividing sets. 131 C17. The minimum overlap problem. 132
C18. The n queens problem. 133 C19. Is a weakly independent
sequence the finite union of strongly independent ones? 135 C20. Sums
of squares. 136
D. Diophantine Equations 139
Dl. Sums of like powers. Euler s conjecture. 139 D2. The Fermat
problem. 144 D3. Figurate numbers. 146 D4. Sums of I fcth
powers. 150 D5. Sum of four cubes. 151 D6. An elementary solution
Contents xi
of x2 = 2y4 — 1. 152 D7. Sum of consecutive powers made a power. 153
D8. A pyramidal diophantine equation. 154 D9. Difference of two
powers. 155 D10. Exponential diophantine equations. 151
Dll. Egyptian fractions. 158 D12. Markoff numbers. 166 D13. The
equation xxyy = zz. 168 D14. ai + bj made squares. 169
D15. Numbers whose sums in pairs make squares. 170 D16. Triples
with the same sum and same product. Ill D17. Product of blocks of
consecutive integers not a power. 112 D18. Is there a perfect cuboid?
Four squares whose sums in pairs are square. Four squares whose
differences are square. 113 D19. Rational distances from the corners of
a square. 181 D20. Six general points at rational distances. 185
D21. Triangles with integer sides, medians and area. 188
D22. Simplexes with rational contents. 190 D23. Some quartic
equations. 191 D24. Sum equals product. 193 D25. Equations
involving factorial n. 193 D26. Fibonacci numbers of various
shapes. 194 D27. Congruent numbers. 195 D28. A reciprocal
diophantine equation. 191
E. Sequences of Integers 199
El. A thin sequence with all numbers equal to a member plus a
prime. 199 E2. Density of a sequence with l.c.m. of each pair less than
x. 200 E3. Density of integers with two comparable divisors. 201
E4. Sequence with no member dividing the product of r others. 201
E5. Sequence with members divisible by at least one of a given set. 202
E6. Sequence with sums of pairs not members of a given sequence. 203
E7. A series and a sequence involving primes. 203 E8. Sequence with
no sum of a pair a square. 203 E9. Partitioning the integers into classes
with numerous sums of pairs. 204 E10. Theorem of van der Waerden.
Szemeredi s theorem. Partitioning the integers into classes; at least one
contains an A.P. 204 Ell. Schur s problem. Partitioning integers into
sum free classes. 209 E12. The modular version of Schur s problem. 211
E13. Partitioning into strongly sum free classes. 213 E14. Rado s
generalizations of van der Waerden s and Schur s problems. 213 E15. A
recursion of Gobel. 214 E16. Collatz s sequence. 215
E17. Permutation sequences. 218 E18. Mahler s Z numbers. 219
E19. Are the integer parts of the powers of a fraction infinitely often
prime? 220 E20. Davenport Schinzel sequences. 220 E21. Thue
sequences. 222 E22. Cycles and sequences containing all permutations
as subsequences. 224 E23. Covering the integers with A.P.s. 224
E24. Irrationality sequences. 225 E25. Silverman s sequence. 225
E26. Epstein s Put or Take a Square game. 226 E27. Max and mex
sequences. 221 E28. B2 sequences. 228 E29. Sequence with sums
and products all in one of two classes. 229 E30. MacMahon s prime
numbers of measurement. 230 E31. Three sequences of Hofstadter. 231
E32. B2 sequences formed by the greedy algorithm. 232
xii Contents
E33. Sequences containing no monotone A.P.s. 233 E34. Happy
numbers. 234 E35. The Kimberling shuffle. 235 E36. Klarner Rado
sequences. 231 E37. Mousetrap. 231 E38. Odd sequences. 238
F. None of the Above 240
Fl. Gaufi s lattice point problem. 240 F2. Lattice points with distinct
distances. 241 F3. Lattice points, no four on a circle. 241 F4. The
no three in line problem. 242 F5. Quadratic residues. Schur s
conjecture. 244 F6. Patterns of quadratic residues. 245 F7. A cubic
analog of a Pell equation. 248 F8. Quadratic residues whose differences
are quadratic residues. 248 F9. Primitive roots 248 F10. Residues of
powers of two. 249 Fll. Distribution of residues of factorials. 250
F12. How often are a number and its inverse of opposite parity? 251
F13. Covering systems of congruences. 251 F14. Exact covering
systems. 253 F15. A problem of R. L. Graham. 256 F16. Products
of small prime powers dividing n. 256 F17. Series associated with the
^ function. 251 F18. Size of the set of sums and products of a set. 258
F19. Partitions into distinct primes with maximum product. 258
F20. Continued fractions. 259 F21. All partial quotients one or
two. 259 F22. Algebraic numbers with unbounded partial
quotients. 260 F23. Small differences between powers of 2 and 3. 261
F24. Squares with just two different decimal digits. 262 F25. The
persistence of a number. 262 F26. Expressing numbers using just
ones. 263 F27. Mahler s generalization of Farey series. 263 F28. A
determinant of value one. 265 F29. Two congruences, one of which is
always solvable. 266 F30. A polynomial whose sums of pairs of values
are all distinct. 266 F31. An unusual digital problem. 266
Index of Authors Cited 268
General Index 280
|
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.7 |
| dewey-sort | 3512 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV009654900 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:38:40Z |
| institution | BVB |
| isbn | 3540942890 0387942890 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006383992 |
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| physical | XVI, 285 S. graph. Darst. |
| publishDate | 1994 |
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| publisher | Springer |
| record_format | marc |
| series | Unsolved problems in intuitive mathematics |
| series2 | Unsolved problems in intuitive mathematics Problem books in mathematics |
| spelling | Guy, Richard K. 1916-2020 Verfasser (DE-588)124655254 aut Unsolved problems in number theory Richard K. Guy 2. ed. New York u.a. Springer 1994 XVI, 285 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Unsolved problems in intuitive mathematics 1 Problem books in mathematics Getaltheorie gtt Nombres, Théorie des Problemen gtt Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Ungelöstes Problem (DE-588)4186869-9 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Zahlentheorie (DE-588)4067277-3 s DE-604 Ungelöstes Problem (DE-588)4186869-9 s Unsolved problems in intuitive mathematics 1 (DE-604)BV001894954 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006383992&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Guy, Richard K. 1916-2020 Unsolved problems in number theory Unsolved problems in intuitive mathematics Getaltheorie gtt Nombres, Théorie des Problemen gtt Number theory Zahlentheorie (DE-588)4067277-3 gnd Ungelöstes Problem (DE-588)4186869-9 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4186869-9 (DE-588)4143389-0 |
| title | Unsolved problems in number theory |
| title_auth | Unsolved problems in number theory |
| title_exact_search | Unsolved problems in number theory |
| title_full | Unsolved problems in number theory Richard K. Guy |
| title_fullStr | Unsolved problems in number theory Richard K. Guy |
| title_full_unstemmed | Unsolved problems in number theory Richard K. Guy |
| title_short | Unsolved problems in number theory |
| title_sort | unsolved problems in number theory |
| topic | Getaltheorie gtt Nombres, Théorie des Problemen gtt Number theory Zahlentheorie (DE-588)4067277-3 gnd Ungelöstes Problem (DE-588)4186869-9 gnd |
| topic_facet | Getaltheorie Nombres, Théorie des Problemen Number theory Zahlentheorie Ungelöstes Problem Aufgabensammlung |
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