Catalan's Intriguing Factorial Problem

Autor/in	Koshy, Thomas
Titel	Catalan's Intriguing Factorial Problem
Quelle	In: International Journal of Mathematical Education in Science and Technology, 43 (2012) 1, S.101-109 (9 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2011.562322
Schlagwörter	Algebra; Numbers; Geometric Concepts; Mathematical Logic; Validity; Mathematics Education; Computation; Problem Solving; Mathematics Instruction; Theories; College Mathematics + Suchen Sie Ihr Suchwort? Zahlenraum; Elementare Geometrie; Mathematical logics; Mathematische Logik; Gültigkeit; Mathematische Bildung; Problemlösen; Mathematics lessons; Mathematikunterricht; Theory; Theorie
Abstract	This article investigates the numbers [image omitted], originally studied by Catalan. We re-confirm that they are indeed integers. Using the close relationship between them and the Catalan numbers C[subscript n], we develop some divisibility properties for C[subscript n]. In particular, we establish that [image omitted], where f[subscript k] denotes the "k"th Fermat number 2[superscript 2[superscript k]] + 1 and M[subscript k] the "k"th Mersenne number 2[superscript k] - 1. Finally, we develop an explicit formula for X[subscript m,n] using Pascal's triangle and Catalan numbers, and extract several interesting byproducts from it. (Contains 1 table.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10