ERIC Number: EJ1108350
Record Type: Journal
Publication Date: 2016
Abstractor: As Provided
All Square Chiliagonal Numbers
A?iru, Muniru A.
International Journal of Mathematical Education in Science and Technology, v47 n7 p1123-1134 2016
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.
Descriptors: Mathematics Instruction, Mathematical Concepts, Equations (Mathematics), Numbers, Problem Solving
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Publication Type: Journal Articles; Reports - Descriptive
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