Geodesic
FFF. Fibonacci: di Fiore in Fiore
Bollettino della Unione matematica italiana, Série 8, 5A (2002) no. 2, pp. 329-353.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In occasione della commemorazione dell’800-esimo anniversario della pubblicazione del Liber Abaci, desidero richiamare l’attenzione del lettore su alcuni dei fatti che preferisco riguardanti numeri di Fibonacci. Tali fatti includono la presenza di quadrati, di multipli di quadrati e di numeri potenti tra i numeri di Fibonacci, la rappresentazione di numeri reali e la costruzione di numeri trascendenti mediante numeri di Fibonacci, la possibilità di costruire una serie zeta ed un dominio a fattorizzazione unica associati ai numeri di Fibonacci 
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Ribenboim, Paulo. FFF. Fibonacci: di Fiore in Fiore. Bollettino della Unione matematica italiana, Série 8, 5A (2002) no. 2, pp. 329-353. http://geodesic.mathdoc.fr/item/BUMI_2002_8_5A_2_a4/

[Ho69] V. E. Hoggatt, Fibonacci and Lucas Numbers, Houghton-Mifflin, Boston (1969). | Zbl

[Vo63] N. N. Vorob’Ev, The Fibonacci numbers, D. C. Heath, Boston (1963). | MR | Zbl

[AJ91] R. Andre-Jeannin, A note on the irrationality of certain Lucas infinite series, Fibonacci Q., 29 (1991), 132-136. | MR | Zbl

[BMS88] J. Brillhart - P. L. Montgomery - R. D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp., 50 (1983), 251-260. | DOI | MR | Zbl

[Ca13] R. D. Carmichael, On the numerical factors of arithmetic forms \({\alpha}^n \pm {\beta}^n\), Annals of Math. (2), 15 (1913), 30-70. | Jbk 44.0216.01 | DOI | MR

[CE63] E. D. Cashwell - C. J. Everett, Formal power series, Pacific J. Math., 13 (1963), 45-69. | fulltext mini-dml | MR | Zbl

[Co64a] J. H. E. Cohn, On square Fibonacci numbers, J. London Math. Soc., 39 (1964), 537-540. | MR | Zbl

[Co64b] J. H. E. Cohn, Square Fibonacci numbers, etc., Fibonacci Q., 2 (1964), 109-113. | MR | Zbl

[Co65] J. H. E. Cohn, Lucas and Fibonacci numbers and some Diophantine equations, Proc. Glasgow Math. Assoc., 7 (1965), 24-28. | MR | Zbl

[El91] N. D. Elkies, (ABC) implies Mordell, Intern. Math. Res. Notices, 7 (1991), 99-109. | DOI | MR | Zbl

[Ha66] J. H. Halton, On the divisibility properties of Fibonacci numbers, Fibonacci Quart., 4 (1966), 217-240. | MR | Zbl

[Kn64] D. Knuth, Transcendental numbers based on the Fibonacci numbers, Fibonacci Q., 2 (1964), 43-44. | Zbl

[LW81] J. C. Lagarias - D. P. Weissel, Fibonacci and Lucas cubes, Fibonacci Q., 19 (1981), 39-43. | MR | Zbl

[LF69] H. London - R. Finkelstein, On Fibonacci and Lucas numbers which are perfect powers, Fibonacci Q., 7 (1969), 476-481 e 487. | MR | Zbl

[Lu78] E. Lucas, Théorie des fonctions numériques simplement périodiques, American J. Math., 1 (1878), 184-240, 289-321. | Jbk 10.0134.05 | DOI | MR

[Ma85] D. W. Masser, Open problems, Proc. Symp. Anal. Number Theory (W. W. W. L. Chern editor), Imperial College, London (1985).

[McR98] W. L. Mc Daniel - P. Ribenboim, Square classes in Lucas sequences, J. Number Theory, 73 (1998), 14-27. | DOI | MR | Zbl

[Mo96] R. A. Mollin, Masser’s conjecture used to prove results about powerful numbers, J. Math. Sci., 7 (1996), 29-32. | MR

[Oe88] J. Oesterle, Nouvelles approches du «théorème» de Fermat, Sém. Bourbaki 694, Astérisque, 161-162 (1988), 165-186. | fulltext EuDML | fulltext mini-dml | MR | Zbl

[Pe82] A. Petho, Perfect powers in second order linear recurrences, J. Number Theory, 15 (1982), 5-13. | DOI | MR | Zbl

[Pe83] A. Petho, Full cubes in the Fibonacci sequence, Publ. Math. Debrecen, 30 (1983), 117-127. | MR | Zbl

[Ri89] P. Ribenboim, Representations of real numbers by means of Fibonacci numbers, Enseign. Math., 31 (1989), 249-259. | MR | Zbl

[Ri95] P. Ribenboim, The Fibonacci numbers and the Arctic Ocean, Symp. Gaussiana, Conf. A (M. Behara, R. Fritsch and R. G. Lintz editors) (1995), 41-83. | MR | Zbl

[Ri96] P. Ribenboim, The New Book of Prime Number Records, Springer Verlag, New York (1996). | DOI | MR | Zbl

[Ri99] P. Ribenboim, An algorithm to determine the points with integral coordinates in certain elliptic curves, J. Number Theory, 74 (1999), 19-39. | DOI | MR | Zbl

[Ri00] P. Ribenboim, My Numbers, my Friends, Springer-Verlag, New York (2000). | MR | Zbl

[Ri01a] P. Ribenboim, ABC candies, J. Number Theory, 81 (2001), 47-60. | MR | Zbl

[Ri01b] P. Ribenboim, The (ABC) conjecture and the radical index of integers, Acta Arith., 96 (2001), 389-404. | DOI | MR | Zbl

[RMc96] P. Ribenboim - W. L. Mc Daniel, The square terms in Lucas sequences, J. Number Theory, 58 (1996), 104-123. | DOI | MR | Zbl

[RW99] P. Ribenboim - P. G. Walsh, The ABC conjecture and the powerful part of terms in binary recurring sequences, J. Number Theory, 74 (1999), 134-147. | DOI | MR | Zbl

[SS83] T. N. Shorey - C. L. Stewart, On the Diophantine equation \(ax^{2}t+ bx^‰{t}y+cy^{2}=1\) and pure powers in recurrence sequences, Math. Scand., 52 (1983), 24-36. | fulltext EuDML | MR | Zbl

[Wy64] O. Wyler, Squares in the Fibonacci series, Amer. Math. Monthly, 7 (1964), 220-222.