B. Bibliography
Here are the works cited in this book. Numbers in the margin specify the page numbers where citations occur.
“This paper fills a much-needed gap in the literature.”
— Math. Reviews
References to published problems are generally made to the places where solutions can be found, instead of to the original problem statements.
Wherever possible, names and titles are spelled here as they appeared in the original publication.
1. N. H. Abel, letter to B. Holmboe (1823), in his Œuvres Complètes, first edition, 1839, volume 2, 264–265. Reprinted in the second edition, 1881, volume 2, 254–255.
634.
2. Milton Abramowitz and Irene A. Stegun, editors, Handbook of Mathematical Functions. United States Government Printing Office, 1964. Reprinted by Dover, 1965.
42.
3. William W. Adams and J. L. Davison, “A remarkable class of continued fractions,” Proceedings of the American Mathematical Society 65 (1977), 194–198. [See also P. E. Böhmer, “Über die Transzendenz gewisser dyadischer Brüche,” Mathematische Annalen 96 (1927), 367–377, 735.]
635.
4. A. V. Aho and N. J. A. Sloane, “Some doubly exponential sequences,” Fibonacci Quarterly 11 (1973), 429–437.
633.
5. W. Ahrens, Mathematische Unterhaltungen und Spiele. Teubner, Leipzig, 1901. Second edition, in two volumes, 1910 and 1918.
8.
6. Naum Il’ich Akhiezer, 
problema momentov i nekotorye voprosy analiza, 
. Moscow, 1961. English translation, The Classical Moment Problem and Some Related Questions in Analysis, Hafner, 1965.
591.
7. R. E. Allardice and A. Y. Fraser, “La Tour d’Hanoï,” Proceedings of the Edinburgh Mathematical Society 2 (1884), 50–53.
2.
8. Désiré André, “Sur les permutations alternées,” Journal de Mathématiques pures et appliquées, series 3, 7 (1881), 167–184.
635.
9. George E. Andrews, “Applications of basic hypergeometric functions,” SIAM Review 16 (1974), 441–484.
10. George E. Andrews, “On sorting two ordered sets,” Discrete Mathematics 11 (1975), 97–106.
530.
11. George E. Andrews, The Theory of Partitions. Addison–Wesley, 1976.
330.
12. George E. Andrews, “Euler’s ‘exemplum memorabile inductionis fallacis’ and q-trinomial coefficients,” Journal of the American Mathematical Society 3 (1990), 653–669.
575.
13. George E. Andrews and K. Uchimura, “Identities in combinatorics IV: Differentiation and harmonic numbers,” Utilitas Mathematica 28 (1985), 265–269.
635.
14. Roger Apéry, “Interpolation de fractions continues et irrationalité de certaines constantes,” in Mathématiques, Ministère des universités (France), Comité des travaux historiques et scientifiques, Section des sciences, Bulletin de la Section des Sciences 3 (1981), 37–53.
15. M. D. Atkinson, “The cyclic towers of Hanoi,” Information Processing Letters 13 (1981), 118–119.
633.
16. M. D. Atkinson, “How to compute the series expansions of sec x and tan x,” American Mathematical Monthly 93 (1986), 387–389. [This triangle was first found by L. Seidel, “Ueber eine einfache Entstehungsweise der Bernoulli’schen Zahlen und einiger verwandten Reihen,” Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München 7 (1877), 157–187.]
635.
17. Paul Bachmann, Die analytische Zahlentheorie. Teubner, Leipzig, 1894.
443.
18. W. N. Bailey, Generalized Hypergeometric Series. Cambridge University Press, 1935; second edition, 1964.
19. W. N. Bailey, “The generating function for Jacobi polynomials,” Journal of the London Mathematical Society 13 (1938), 243–246.
548.
19′ R. Balasubramanian and K. Soundararajan, “On a conjecture of R. L. Graham,” Acta Arithmetica 75 (1996), 1–38.
525.
20. W. W. Rouse Ball and H. S. M. Coxeter, Mathematical Recreations and Essays, twelfth edition. University of Toronto Press, 1974. (A revision of Ball’s Mathematical Recreations and Problems, first published by Macmillan, 1892.)
633.
21. P. Barlow, “Demonstration of a curious numerical proposition,” Journal of Natural Philosophy, Chemistry, and the Arts 27 (1810), 193–205.
634.
22. Samuel Beatty, “Problem 3177,” American Mathematical Monthly 34 (1927), 159–160.
633.
23. E. T. Bell, “Euler algebra,” Transactions of the American Mathematical Society 25 (1923), 135–154.
332.
24. E. T. Bell, “Exponential numbers,” American Mathematical Monthly 41 (1934), 411–419.
635.
25. Edward A. Bender, “Asymptotic methods in enumeration,” SIAM Review 16 (1974), 485–515.
636.
26. Jacobi Bernoulli, Ars Conjectandi, opus posthumum. Basel, 1713. Reprinted in Die Werke von Jakob Bernoulli, volume 3, 107–286.
283.
27. J. Bertrand, “Mémoire sur le nombre de valeurs que peut prendre une fonction quand on y permute les lettres qu’elle renferme,” Journal de l’École Royale Polytechnique 18, cahier 30 (1845), 123–140.
633.
28. William H. Beyer, editor, CRC Standard Mathematical Tables and Formulae, 29th edition. CRC Press, Boca Raton, Florida, 1991.
42.
29. J. Bienaymé, “Considérations à l’appui de la découverte de Laplace sur la loi de probabilité dans la méthode des moindres carrés,” Comptes Rendus hebdomadaires des séances de l’Académie des Sciences (Paris) 37 (1853), 309–324.
390.
30. J. Binet, “Mémoire sur un système de Formules analytiques, et leur application à des considérations géométriques,” Journal de l’École Polytechnique 9, cahier 16 (1812), 280–354.
633.
31. J. Binet, “Mémoire sur l’intégration des équations linéaires aux différences finies, d’un ordre quelconque, à coefficients variables,” Comptes Rendus hebdomadaires des séances de l’Académie des Sciences (Paris) 17 (1843), 559–567.
299.
32. Gunnar Blom, “Problem E 3043: Random walk until no shoes,” American Mathematical Monthly 94 (1987), 78–79.
636.
33. R. P. Boas, Jr. and J. W. Wrench, Jr., “Partial sums of the harmonic series,” American Mathematical Monthly 78 (1971), 864–870.
34. P. Bohl, “Über ein in der Theorie der säkularen Störungen vorkommendes Problem,” Journal für die reine und angewandte Mathematik 135 (1909), 189–283.
87.
35. Émile Borel, Leçons sur les séries à termes positifs. Paris, 1902.
636.
36. Jonathan M. Borwein and Peter B. Borwein, Pi and the AGM. Wiley, 1987.
635.
37. Richard P. Brent, “The first occurrence of large gaps between successive primes,” Mathematics of Computation 27 (1973), 959–963.
525.
38. Richard P. Brent, “Computation of the regular continued fraction for Euler’s constant,” Mathematics of Computation 31 (1977), 771–777.
39. John Brillhart, “Some miscellaneous factorizations,” Mathematics of Computation 17 (1963), 447–450.
633.
40. Achille Brocot, “Calcul des rouages par approximation, nouvelle méthode,” Revue Chronométrique 3 (1861), 186–194. (He also published a 97-page monograph with the same title in 1862.)
116.
41. Maxey Brooke and C. R. Wall, “Problem B-14: A little surprise,” Fibonacci Quarterly 1, 3 (1963), 80.
635.
42. Brother U. Alfred [Brousseau], “A mathematician’s progress,” Mathematics Teacher 59 (1966), 722–727.
633.
43. Morton Brown, “Problem 6439: A periodic sequence,” American Mathematical Monthly 92 (1985), 218.
501.
44. T. Brown, “Infinite multi-variable subpolynormal Woffles which do not satisfy the lower regular Q-property (Piffles),” in A Collection of 250 Papers on Woffle Theory Dedicated to R. S. Green on His 23rd Birthday. Cited in A. K. Austin, “Modern research in mathematics,” The Mathematical Gazette 51 (1967), 149–150.
(Such papers aren’t cited in this book.)
45. Thomas C. Brown, “Problem E 2619: Squares in a recursive sequence,” American Mathematical Monthly 85 (1978), 52–53.
633.
46. William G. Brown, “Historical note on a recurrent combinatorial problem,” American Mathematical Monthly 72 (1965), 973–977.
358.
47. S. A. Burr, “On moduli for which the Fibonacci sequence contains a complete system of residues,” Fibonacci Quarterly 9 (1971), 497–504.
635.
48. E. Rodney Canfield, “On the location of the maximum Stirling number(s) of the second kind,” Studies in Applied Mathematics 59 (1978), 83–93.
49. L. Carlitz, “The generating function for max(n1, n2, · · · , nk),” Portugaliae Mathematica 21 (1962), 201–207.
635.
50. Lewis Carroll [pseudonym of C. L. Dodgson], Through the Looking Glass and What Alice Found There. Macmillan, 1871.
31.
51. Jean-Dominique Cassini, “Une nouvelle progression de nombres,” Histoire de l’Académie Royale des Sciences, Paris, volume 1, 201. (Cassini’s work is summarized here as one of the mathematical results presented to the academy in 1680. This volume was published in 1733.)
292.
52. E. Catalan, “Note sur une Équation aux différences finies,” Journal de Mathématiques pures et appliquées 3 (1838), 508–516.
203.
53. Augustin-Louis Cauchy, Cours d’analyse de l’École Royale Polytechnique. Imprimerie Royale, Paris, 1821. Reprinted in his Œuvres complètes, series 2, volume 3.
633.
54. Arnold Buffum Chace, The Rhind Mathematical Papyrus, volume 1. Mathematical Association of America, 1927. (Includes an excellent bibliography of Egyptian mathematics by R. C. Archibald.)
633.
55. M. Chaimovich, G. Freiman, and J. Schönheim, “On exceptions to Szegedy’s theorem,” Acta Arithmetica 49 (1987), 107–112.
525.
56. P. L. Tchebichef [Chebyshev], “Mémoire sur les nombres premiers,” Journal de Mathématiques pures et appliquées 17 (1852), 366–390. Reprinted in his Œuvres, volume 1, 51–70. Russian translation, “O prostykh chislakh,” in his Polnoe sobranie sochinenĭı, volume 1, 191–207.
633.
57. P. L. Chebyshev˝, “O srednikh˝ velichinakh˝,” Matematicheskiĭ Sbornik˝ 2,1 (1867), 1–9. Reprinted in his Polnoe sobranie sochineniĭ, volume 2, 431–437. French translation, “Des valeurs moyennes,” Journal de Mathématiques pures et appliquées, series 2, 12 (1867), 177–184; reprinted in his Œuvres, volume 1, 685–694.
390.
58. P. L. Chebyshev˝, “O priblizhennykh˝ 
odnikh˝ integralov˝ cherez˝ drugīe, 
v˝ 
zhe 
,” 
i protokoly 
matematicheskago obshchestva pri Imperatorskom˝ Khar’kovskom˝ 
4,2 (1882), 93–98. Reprinted in his Polnoe sobranie sochinenĭı, volume 3, 128–131. French translation, “Sur les expressions approximatives des intégrales définies par les autres prises entre les mêmes limites,” in his Œuvres, volume 2, 716–719.
38.
59. F. R. K. Chung and R. L. Graham, “On the cover polynomial of a digraph,” Journal of Combinatorial Theory, series B, 65 (1995), 273–290.
60. Th. Clausen, “Ueber die Fälle, wenn die Reihe von der Form
634.
ein Quadrat von der Form
Journal für die reine und angewandte Mathematik 3 (1828), 89–91.
61. Th. Clausen, “Beitrag zur Theorie der Reihen,” Journal für die reine und angewandte Mathematik 3 (1828), 92–95.
634.
62. Th. Clausen, “Theorem,” Astronomische Nachrichten 17 (1840), columns 351–352.
635.
63. Stuart Dodgson Collingwood, The Lewis Carroll Picture Book. T. Fisher Unwin, 1899. Reprinted by Dover, 1961, with the new title Diversions and Digressions of Lewis Carroll.
293.
64. Louis Comtet, Advanced Combinatorics. Dordrecht, Reidel, 1974.
636.
65. J. H. Conway and R. L. Graham, “Problem E 2567: A periodic recurrence,” American Mathematical Monthly 84 (1977), 570–571.
501.
66. Harald Cramér, “On the order of magnitude of the difference between consecutive prime numbers,” Acta Arithmetica 2 (1937), 23–46.
67. A. L. Crelle, “Démonstration élémentaire du théorème de Wilson généralisé,” Journal für die reine und angewandte Mathematik 20 (1840), 29–56.
633.
68. D. W. Crowe, “The n-dimensional cube and the Tower of Hanoi,” American Mathematical Monthly 63 (1956), 29–30.
633.
69. János A. Csirik, “Optimal strategy for the first player in the Penney ante game,” Combinatorics, Probability and Computing 1 (1992), 311–321.
590.
70. D. R. Curtiss, “On Kellogg’s Diophantine problem,” American Mathematical Monthly 29 (1922), 380–387.
634.
71. F. N. David and D. E. Barton, Combinatorial Chance. Hafner, 1962.
602.
72. Philip J. Davis, “Leonhard Euler’s integral: A historical profile of the Gamma function,” American Mathematical Monthly 66 (1959), 849–869.
210.
73. J. L. Davison, “A series and its associated continued fraction,” Proceedings of the American Mathematical Society 63 (1977), 29–32.
74. N. G. de Bruijn, Asymptotic Methods in Analysis. North-Holland, 1958; third edition, 1970. Reprinted by Dover, 1981.
75. N. G. de Bruijn, “Problem 9,” Nieuw Archief voor Wiskunde, series 3, 12 (1964), 68.
635.
76. Abraham de Moivre, Miscellanea analytica de seriebus et quadraturis. London, 1730.
77. R. Dedekind, “Abriß einer Theorie der höheren Congruenzen in Bezug auf einen reellen Primzahl-Modulus,” Journal für die reine und angewandte Mathematik 54 (1857), 1–26. Reprinted in his Gesammelte mathematische Werke, volume 1, 40–67.
136.
78. Leonard Eugene Dickson, History of the Theory of Numbers. Carnegie Institution of Washington, volume 1, 1919; volume 2, 1920; volume 3, 1923. Reprinted by Stechert, 1934, and by Chelsea, 1952, 1971.
510.
79. Edsger W. Dijkstra, Selected Writings on Computing: A Personal Perspective. Springer-Verlag, 1982.
635.
80. G. Lejeune Dirichlet, “Verallgemeinerung eines Satzes aus der Lehre von den Kettenbrüchen nebst einigen Anwendungen auf die Theorie der Zahlen,” Bericht über die Verhandlungen der Königlich-Preußischen Akademie der Wissenschaften zu Berlin (1842), 93–95. Reprinted in his Werke, volume 1, 635–638.
633.
81. A. C. Dixon, “On the sum of the cubes of the coefficients in a certain expansion by the binomial theorem,” The Messenger of Mathematics, new series, 20 (1891), 79–80.
634.
82. John Dougall, “On Vandermonde’s theorem, and some more general expansions,” Proceedings of the Edinburgh Mathematical Society 25 (1907), 114–132.
171.
83. A. Conan Doyle, “The sign of the four; or, The problem of the Sholtos,” Lippincott’s Monthly Magazine (Philadelphia) 45 (1890), 145–223.
84. A. Conan Doyle, “The adventure of the final problem,” The Strand Magazine 6 (1893), 558–570.
162.
85. P. du Bois-Reymond, “Sur la grandeur relative des infinis des fonctions,” Annali di Matematica pura ed applicata, series 2, 4 (1871), 338–353.
440.
86. Harvey Dubner, “Generalized repunit primes,” Mathematics of Computation 61 (1993), 927–930.
633.
87. Henry Ernest Dudeney, The Canterbury Puzzles and Other Curious Problems. E. P. Dutton, New York, 1908; 4th edition, Dover, 1958. (Dudeney had first considered the generalized Tower of Hanoi in The Weekly Dispatch, on 15 November 1896, 25 May 1902, and 15 March 1903.)
633.
88. G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science. Exposition Press, New York, 1955.
6.
89. F. J. Dyson, “Some guesses in the theory of partitions,” Eureka 8 (1944), 10–15.
239.
90. A. W. F. Edwards, Pascal’s Arithmetical Triangle. Oxford University Press, 1987.
155.
91. G. Eisenstein, “Entwicklung von ααα...,” Journal für die reine und angewandte Mathematik 28 (1844), 49–52. Reprinted in his Mathematische Werke 1, 122–125.
202.
92. Noam D. Elkies, “On A4 + B4 + C4 = D4,” Mathematics of Computation 51 (1988), 825–835.
131.
93. Erdős Pál, “
egyenlet egész számú meg oldásairól,” Matematikai Lapok 1 (1950), 192–209. English abstract on page 210.
634.
94. Paul Erdös, “My Scottish Book ‘problems’,” in The Scottish Book: Mathematics from the Scottish Café, edited by R. Daniel Mauldin, 1981, 35–45.
418.
95. P. Erdös and R. L. Graham, Old and New Problems and Results in Combinatorial Number Theory. Université de Genève, L’Enseignement Mathématique, 1980.
96. P. Erdös, R. L. Graham, I. Z. Ruzsa, and E. G. Straus, “On the prime factors of 
,” Mathematics of Computation 29 (1975), 83–92.
97. Arulappah Eswarathasan and Eugene Levine, “p-integral harmonic sums,” Discrete Mathematics 91 (1991), 249–257.
635.
98. Euclid, ΣTOIXEIA. Ancient manuscript first printed in Basel, 1533. Scholarly edition (Greek and Latin) by J. L. Heiberg in five volumes, Teubner, Leipzig, 1883–1888.
108.
99. Leonhard Euler, letter to Christian Goldbach (13 October 1729), in Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle, edited by P. H. Fuss, St. Petersburg, 1843, volume 1, 3–7.
100. L. Eulero, “De progressionibus transcendentibus seu quarum termini generales algebraice dari nequeunt,” Commentarii academiæ scientiarum imperialis Petropolitanæ 5 (1730), 36–57. Reprinted in his Opera Omnia, series 1, volume 14, 1–24.
210.
101. Leonh. Eulero, “Methodus generalis summandi progressiones,” Commentarii academiæ scientiarum imperialis Petropolitanæ 6 (1732), 68–97. Reprinted in his Opera Omnia, series 1, volume 14, 42–72.
469.
102. Leonh. Eulero, “Observationes de theoremate quodam Fermatiano, aliisque ad numeros primos spectantibus,” Commentarii academiæ scientiarum imperialis Petropolitanæ 6 (1732), 103–107. Reprinted in his Opera Omnia, series 1, volume 2, 1–5. Reprinted in his Commentationes arithmeticæ collectæ, volume 1, 1–3.
132.
103. Leonh. Eulero, “De progressionibus harmonicis observationes,” Commentarii academiæ scientiarum imperialis Petropolitanæ 7 (1734), 150–161. Reprinted in his Opera Omnia, series 1, volume 14, 87–100.
104. Leonh. Eulero, “Methodus universalis series summandi ulterius promota,” Commentarii academiæ scientiarum imperialis Petropolitanæ 8 (1736), 147–158. Reprinted in his Opera Omnia, series 1, volume 14, 124–137.
267.
105. Leonh. Euler, “De fractionibus continuis, Dissertatio,” Commentarii academiæ scientiarum imperialis Petropolitanæ 9 (1737), 98–137. Reprinted in his Opera Omnia, series 1, volume 14, 187–215.
122.
106. Leonh. Euler, “Variæ observationes circa series infinitas,” Commentarii academiæ scientiarum imperialis Petropolitanæ 9 (1737), 160–188. Reprinted in his Opera Omnia, series 1, volume 14, 216–244.
633.
107. Leonhard Euler, letter to Christian Goldbach (4 July 1744), in Correspondance mathématique et physique de quelques célèbres géomètres du XVIIIème siècle, edited by P. H. Fuss, St. Petersburg, 1843, volume 1, 278–293.
603.
108. Leonhardo Eulero, Introductio in Analysin Infinitorum. Tomus primus, Lausanne, 1748. Reprinted in his Opera Omnia, series 1, volume 8. Translated into French, 1786; German, 1788; Russian, 1936; English, 1988.
635.
109. L. Eulero, “De partitione numerorum,” Novi commentarii academiæ scientiarum imperialis Petropolitanæ 3 (1750), 125–169. Reprinted in his Commentationes arithmeticæ collectæ, volume 1, 73–101. Reprinted in his Opera Omnia, series 1, volume 2, 254–294.
635.
110. Leonhardo Eulero, Institutiones Calculi Differentialis cum eius usu in Analysi Finitorum ac Doctrina Serierum. St. Petersburg, Academiæ Imperialis Scientiarum Petropolitanæ, 1755. Reprinted in his Opera Omnia, series 1, volume 10. Translated into German, 1790.
111. L. Eulero, “Theoremata arithmetica nova methodo demonstrata,” Novi commentarii academiæ scientiarum imperialis Petropolitanæ 8 (1760), 74–104. (Also presented in 1758 to the Berlin Academy.) Reprinted in his Commentationes arithmeticæ collectæ, volume 1, 274–286. Reprinted in his Opera Omnia, series 1, volume 2, 531–555.
112. L. Eulero, “Specimen algorithmi singularis,” Novi commentarii academiæ scientiarum imperialis Petropolitanæ 9 (1762), 53–69. (Also presented in 1757 to the Berlin Academy.) Reprinted in his Opera Omnia, series 1, volume 15, 31–49.
113. L. Eulero, “Observationes analyticæ,” Novi commentarii academiæ scientiarum imperialis Petropolitanæ 11 (1765), 124–143. Reprinted in his Opera Omnia, series 1, volume 15, 50–69.
114. Leonhard Euler, Vollständige Anleitung zur Algebra. Erster Theil. Von den verschiedenen Rechnungs-Arten, Verhältnissen und Proportionen. St. Petersburg, 1770. Reprinted in his Opera Omnia, series 1, volume 1. Translated into Russian, 1768; Dutch, 1773; French, 1774; Latin, 1790; English, 1797.
636.
115. L. Eulero, “Observationes circa bina biquadrata quorum summam in duo alia biquadrata resolvere liceat,” Novi commentarii academiæ scientiarum imperialis Petropolitanæ 17 (1772), 64–69. Reprinted in his Commentationes arithmeticæ collectæ, volume 1, 473–476. Reprinted in his Opera Omnia, series 1, volume 3, 211–217.
131.
116. L. Eulero, “Observationes circa novum et singulare progressionum genus,” Novi commentarii academiæ scientiarum imperialis Petropolitanæ 20 (1775), 123–139. Reprinted in his Opera Omnia, series 1, volume 7, 246–261.
513.
117. L. Eulero, “De serie Lambertina, plurimisque eius insignibus proprietatibus,” Acta academiæ scientiarum imperialis Petropolitanæ 3,2 (1779), 29–51. Reprinted in his Opera Omnia, series 1, volume 6, 350–369.
202.
118. L. Eulero, “Specimen transformationis singularis serierum,” Nova acta academiæ scientiarum imperialis Petropolitanæ 12 (1794), 58–70. Submitted for publication in 1778. Reprinted in his Opera Omnia, series 1, volume 16(2), 41–55.
119. Johann Faulhaber, Academia Algebræ, Darinnen die miraculosische Inventiones zu den höchsten Cossen weiters continuirt und profitiert werden, . . . biß auff die regulierte Zensicubiccubic Coß durch offnen Truck publiciert worden. Augsburg, 1631.
288.
120. William Feller, An Introduction to Probability Theory and Its Applications, volume 1. Wiley, 1950; second edition, 1957; third edition, 1968.
121. Pierre de Fermat, letter to Marin Mersenne (25 December 1640), in Œuvres de Fermat, volume 2, 212–217.
131.
122. Leonardo filio Bonacii Pisano [Fibonacci], Liber Abaci. First edition, 1202 (now lost); second edition, 1228. Reprinted in Scritti di Leonardo Pisano, edited by Baldassarre Boncompagni, 1857, volume 1.
123. Bruno de Finetti, Teoria delle Probabilità. Turin, 1970. English translation, Theory of Probability, Wiley, 1974–1975.
24.
124. Michael E. Fisher, “Statistical mechanics of dimers on a plane lattice,” Physical Review 124 (1961), 1664–1672.
636.
125. R. A. Fisher, “Moments and product moments of sampling distributions,” Proceedings of the London Mathematical Society, series 2, 30 (1929), 199–238.
636.
126. Pierre Forcadel, L’arithmeticque. Paris, 1557.
634.
127. J. Fourier, “Refroidissement séculaire du globe terrestre,” Bulletin des Sciences par la Société philomathique de Paris, series 3, 7 (1820), 58–70. Reprinted in Œuvres de Fourier, volume 2, 271–288.
22.
128. Aviezri S. Fraenkel, “Complementing and exactly covering sequences,” Journal of Combinatorial Theory, series A, 14 (1973), 8–20.
129. Aviezri S. Fraenkel, “How to beat your Wythoff games’ opponent on three fronts,” American Mathematical Monthly 89 (1982), 353–361.
563.
130. J. S. Frame, B. M. Stewart, and Otto Dunkel, “Partial solution to problem 3918,” American Mathematical Monthly 48 (1941), 216–219.
633.
131. Piero della Francesca, Libellus de quinque corporibus regularibus. Vatican Library, manuscript Urbinas 632. Translated into Italian by Luca Pacioli, as part 3 of Pacioli’s Diuine Proportione, Venice, 1509.
635.
132. J. Franel, Solutions to questions 42 and 170, in L’Intermédiaire des Math ématiciens 1 (1894), 45–47; 2 (1895), 33–35.
549.
133. W. D. Frazer and A. C. McKellar, “Samplesort: A sampling approach to minimal storage tree sorting,” Journal of the Association for Computing Machinery 27 (1970), 496–507.
634.
134. Michael Lawrence Fredman, Growth Properties of a Class of Recursively Defined Functions. Ph.D. thesis, Stanford University, Computer Science Department, 1972.
513.
135. Nikolao Fuss, “Solutio quæstionis, quot modis polygonum n laterum in polygona m laterum, per diagonales resolvi quæat,” Nova acta academiæ scientiarum imperialis Petropolitanæ 9 (1791), 243–251.
361.
136. Martin Gardner, “About phi, an irrational number that has some re markable geometrical expressions,” Scientific American 201, 2 (August 1959), 128–134. Reprinted with additions in his book The 2nd Scientific American Book of Mathematical Puzzles & Diversions, 1961, 89–103.
299.
137. Martin Gardner, “On the paradoxical situations that arise from non transitive relations,” Scientific American 231, 4 (October 1974), 120–124. Reprinted with additions in his book Time Travel and Other Mathematical Bewilderments, 1988, 55–69.
410.
138. Martin Gardner, “From rubber ropes to rolling cubes, a miscellany of refreshing problems,” Scientific American 232, 3 (March 1975), 112–114; 232, 4 (April 1975), 130, 133. Reprinted with additions in his book Time Travel and Other Mathematical Bewilderments, 1988, 111–124.
634.
139. Martin Gardner, “On checker jumping, the amazon game, weird dice, card tricks and other playful pastimes,” Scientific American 238, 2 (February 1978), 19, 22, 24, 25, 30, 32. Reprinted with additions in his book Penrose Tiles to Trapdoor Ciphers, 1989, 265–280.
636.
140. J. Garfunkel, “Problem E 1816: An inequality related to Stirling’s formula,” American Mathematical Monthly 74 (1967), 202.
636.
141. George Gasper and Mizan Rahman, Basic Hypergeometric Series. Cambridge University Press, 1990.
223.
142. Carolo Friderico Gauss, Disquisitiones Arithmeticæ. Leipzig, 1801. Reprinted in his Werke, volume 1.
143. Carolo Friderico Gauss, “Disquisitiones generales circa seriem infinitam
Pars prior,” Commentationes societatis regiæ scientiarum Gottingensis recentiores 2 (1813). (Thesis delivered to the Royal Society in Göttingen, 20 January 1812.) Reprinted in his Werke, volume 3, 123–163, together with an unpublished sequel on pages 207–229.
144. C. F. Gauss, “Pentagramma mirificum,” written prior to 1836. Published posthumously in his Werke, volume 3, 480–490.
633.
145. Angelo Genocchi, “Intorno all’espressione generale de’numeri Bernulliani,” Annali di Scienze Matematiche e Fisiche 3 (1852), 395–405.
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