All Square Chiliagonal Numbers

Autor/in	A?iru, Muniru A.
Titel	All Square Chiliagonal Numbers
Quelle	In: International Journal of Mathematical Education in Science and Technology, 47 (2016) 7, S.1123-1134 (12 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2016.1164346
Schlagwörter	Mathematics Instruction; Mathematical Concepts; Equations (Mathematics); Numbers; Problem Solving + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Equations; Mathematics; Gleichungslehre; Zahlenraum; Problemlösen
Abstract	A square chiliagonal number is a number which is simultaneously a chiliagonal number and a perfect square (just as the well-known square triangular number is both triangular and square). In this work, we determine which of the chiliagonal numbers are perfect squares and provide the indices of the corresponding chiliagonal numbers and square numbers. The study revealed that the determination of square chiliagonal numbers naturally leads to a generalized Pell equation x[superscript 2] - Dy[superscript 2] = N with D = 1996 and N = 996[superscript 2], and has six fundamental solutions out of which only three yielded integer values for use as indices of chiliagonal numbers. The crossing/independent recurrence relations satisfied by each class of indices of the corresponding chiliagonal numbers and square numbers are obtained. Finally, the generating functions serve as a clothesline to hang up the indices of the corresponding chiliagonal numbers and square numbers for easy display and this was used to obtain the first few sequence of square chiliagonal numbers. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01