Literaturnachweis - Detailanzeige
Autor/in | Koshy, Thomas |
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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 |
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 |
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 |