The irrationality of certain infinite series
Glasgow mathematical journal, Tome 29 (1987) no. 2, pp. 221-228

Voir la notice de l'article provenant de la source Cambridge University Press

The aim of this paper is to prove the irrationality of a certain class of infinite series. The main theorem is related to some results due to Erdos and Straus [7], Erdos [5] and Sándor [15]. As applications of the main result, the solutions of two problems posed by Erdös and Graham [6] are given, among others.
Badea, C. The irrationality of certain infinite series. Glasgow mathematical journal, Tome 29 (1987) no. 2, pp. 221-228. doi: 10.1017/S0017089500006868
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Badea, C., The irrationality of certain infinite products, to appear in Studia Univ. Babeş-Bolyai Math. Google Scholar

Badea, C., On some problems of Erdos and Graham concerning Fibonacci and Lucas numbers, submitted. Google Scholar

Brun, V., Ein Satz über Irrationalität, Arch, for Math, og Naturvidenskab (Kristiania) 31 (1910), 3. Google Scholar

C&lin, D. and Kiss, V., Irationalitatea sumelor unor serii remarcabile, Gaz. Mat. Ser. A 75 (1970), 161–164. Google Scholar

Erdös, P., Some problems and results on the irrationality of the sum of infinite series, J. Math. Sci. 10 (1975), 1–7. Google Scholar

Erdös, P. and Graham, R. L., Old and new problems and results in combinatorial number theory (Imprimerie Kunding, 1980). Google Scholar

Erdös, P. and Straus, E. G., On the irrationality of certain Ahmes series, J. Indian Math. Soc. 27 (1963), 129–133. Google Scholar

Froda, A., Sur I'irrationalité du nombre 2', Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 35 (1963), 472–478. Google Scholar

Gelbaum, B., Problems in analysis (Springer, 1982). Google Scholar | DOI

Good, I. J., A reciprocal series of Fibonacci numbers, Fibonacci Quart. 12 (1974), 346. Google Scholar

Guy, R. K., Unsolved problems in number theory (Springer, 1981). Google Scholar | DOI

Hoggatt, V. E. Jr, and Bicknell, M., A reciprocal series of Fibonacci numbers with subscripts of 2”k, Fibonacci Quart. 14 (1976), 453–455. Google Scholar

Mahler, K., On the transcendency of the solutions of a special class offunctional equations, Bull. Austral. Math. Soc. 13 (1975), 389–410. Google Scholar | DOI

Mignotte, M., Quelques problèmes d'effectivité en théorie des nombres (Thesis, Univ. Paris • XIII, Paris, 1974). Google Scholar

Sándor, J., Some classes of irrational numbers, Studia Univ. Babeş-Bolyai Math. 29 (1984), 3–12. Google Scholar

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