[1] André-Jeannin, R.:
Irrationalité de la somme des inverses de certaines suites récurrentes. C. R. Acad. Sci. Paris Sér. I Math. 308 (1989), 539–541.
MR 0999451
[3] Brown, J. L.:
Zeckendorf’s theorem and some applications. Fibonacci Quart. 2 (1964), 163–168.
Zbl 0127.27301
[4] Brousseau, A.: Tables of Fibonacci entry points (Parts One and Two). The Fibonacci Association 1965.
[6] Bugeaud, Y., Mignotte, M., Siksek, S.: Classical and modular approaches to exponential diophantine equations, I. Fibonacci and Lucas perfect powers. Submitted to Ann. of Math. (2004).
[7] Calda, E.: Fibonacciova čísla a Pascalův trojúhelník. Rozhledy mat.-fyz. 71 (1993/94), 15–19.
[8] Carmichael, R. D.:
On the numerical factors of the arithmetic forms ${\alpha ^n\pm \beta ^n}$. Ann. Math. 15 (1913), No. 2, 30–70.
MR 1502458
[12] Erdős, P., Graham, R. L.:
Old and new problems and results in combinatorial number theory. Monographie 28 de L’Enseign. Math., Imprimerie Kundig, Genéve 1980.
MR 0592420
[13] Good, I. J.:
A reciprocal series of Fibonacci numbers. Fibonacci Quart. 12 (1974), 346.
MR 0351977 |
Zbl 0292.10009
[14] Halton, J. H.:
On Fibonacci residues. Fibonacci Quart. 2 (1964), 217–218.
Zbl 0119.27905
[15] Henrici, P.:
Discrete variable methods in ordinary differential equations. John Wiley & Sons, New York 1962.
MR 0135729 |
Zbl 0112.34901
[16] Hogben, L.:
An introduction to mathematical genetics. Norton, New York 1946.
MR 0019906
[17] Hoggatt, V. E.:
Fibonacci and Lucas numbers. Houghton Mifflin Company, Boston 1969.
Zbl 0198.36903
[18] Jarden, D.:
Recurring sequences: a collection of papers. Riveon Lematematika, Jerusalem 1973.
MR 0197383
[19] Jones, J. P.:
Diophantine representation of the Fibonacci numbers. Fibonacci Quart. 13 (1975), 84–88.
MR 0382147 |
Zbl 0301.10010
[21] Koshy, T.:
Fibonacci and Lucas numbers with applications. John Wiley & Sons, Inc., New York 2001.
MR 1855020 |
Zbl 0984.11010
[22] Křížek, M., Luca, F., Somer, L.:
17 lectures on Fermat numbers. Springer-Verlag, New York 2001.
MR 1866957 |
Zbl 1010.11002
[23] Křížek, M., Šolcová, A.: Jak spolu souvisí chaos, fraktály a teorie čísel. Sborník semináře Determinismus a chaos, Herbertov 2005, FS ČVUT, Praha 2005, 96–113.
[24] Lagarias, J. C.:
The set of primes dividing the Lucas numbers has density $2/3$. Pacific J. Math. 118 (1985), 449–461. Errata ibid. 162 (1994), 393–396.
MR 0789184 |
Zbl 0569.10003
[25] Lind, D. A.:
The quadratic field ${\mathbb Q}[\sqrt{5}]$ and a certain diophantine equation. Fibonacci Quart. 6 (1968), 86–93.
MR 0231784
[26] Ljunggren, W.:
On the diophantine equation ${x^2+4=Ay^2}$. Det. Kgl. Norske Vid.S̄elsk. Forh. 24 (1951), 82–84.
MR 0049214
[27] London, H., Finkelstein, R.:
On Fibonacci and Lucas numbers which are perfect powers. Fibonacci Quart. 7 (1969), 476–481, 487. Errata ibid. 8 (1970), 248.
MR 0255482 |
Zbl 0206.05402
[28] Luca, F.: Proposed problem H-596. Advanced Problem Section, Fibonacci Quart. 41 (2003), 187.
[31] Luo, M.:
On triangular Fibonacci numbers. Fibonacci Quart. 27 (1989), 98–108.
MR 0995557
[32] Matiyasevich, Y.:
Enumerable sets are diophantine. Soviet Math. Dokl. 11 (1970), 354–358.
Zbl 0212.33401
[34] Matiyasevich, Y. V., Guy, R. K.:
A new formula for $\pi $. Amer. Math. Monthly 93 (1986), 631–635.
MR 1712797 |
Zbl 0614.10003
[35] McDaniel, W.:
On Fibonacci and Pell numbers of the form $kx^2$. Fibonacci Quart. 40 (2002), 41–42.
MR 1885268 |
Zbl 1068.11010
[36] McLaughlin, J.: Small prime powers in the Fibonacci sequence. Preprint, Univ. of Illinois 2002.
[37] Nemes, I., Pethő, A.:
Polynomial values in linear recurrences, II. J. Number Theory 24 (1986), 47–53.
MR 0852189
[38] Pisano, L.:
Fibonacci’s Liber abaci. A translation into modern English of Leonardo Pisano’s Book of calculation. Translated by L. E. Sigler, Springer, New York 2002.
MR 1923794 |
Zbl 1032.01046
[39] Schroeder, M. R.:
Number theory in science and communication. Springer Series in Information Sci. 7, second edition, Springer, Berlin 1986.
MR 0827496 |
Zbl 0613.10001
[40] Stewart, C. L.:
On the representation of an integer in two different bases. J. Reine Angew. Math. 319 (1980), 63–72.
MR 0586115 |
Zbl 0426.10008
[41] Vajda, S.:
Fibonacci & Lucas numbers, and the golden section: Theory and applications. John Wiley & Sons, New York 1989.
MR 1015938 |
Zbl 0695.10001
[45] Zhu, Z., Cao, L., Liu, X., Zhu, W.:
Topological invariance of the Fibonacci sequences of the periodic buds in general Mandelbrot sets. J. Northeast Univ. Na. Sci. 22 (2001), 497–500.
MR 1869910